How many factors of 400 are not multiples of 2

Here we have a collection of all the information you may need about the Prime Factors of 400. We will give you the definition of Prime Factors of 400, show you how to find the Prime Factors of 400 (Prime Factorization of 400) by creating a Prime Factor Tree of 400, tell you how many Prime Factors of 400 there are, and we will show you the Product of Prime Factors of 400.

Prime Factors of 400 definition

First note that prime numbers are all positive integers that can only be evenly divided by 1 and itself. Prime Factors of 400 are all the prime numbers that when multiplied together equal 400.
How to find the Prime Factors of 400 The process of finding the Prime Factors of 400 is called Prime Factorization of 400. To get the Prime Factors of 400, you divide 400 by the smallest prime number possible. Then you take the result from that and divide that by the smallest prime number. Repeat this process until you end up with 1. This Prime Factorization process creates what we call the Prime Factor Tree of 400. See illustration below.

All the prime numbers that are used to divide in the Prime Factor Tree are the Prime Factors of 400. Here is the math to illustrate: 400 ÷ 2 = 200200 ÷ 2 = 100100 ÷ 2 = 5050 ÷ 2 = 2525 ÷ 5 = 55 ÷ 5 = 1 Again, all the prime numbers you used to divide above are the Prime Factors of 400. Thus, the Prime Factors of 400 are: 2, 2, 2, 2, 5, 5.
How many Prime Factors of 400? When we count the number of prime numbers above, we find that 400 has a total of 6 Prime Factors.

Product of Prime Factors of 400

The Prime Factors of 400 are unique to 400. When you multiply all the Prime Factors of 400 together it will result in 400. This is called the Product of Prime Factors of 400. The Product of Prime Factors of 400 is: 2 × 2 × 2 × 2 × 5 × 5 = 400

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Prime Factors of 401

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Question: Children (and adults) are often uncertain whether the multiples of, say, 12 are the numbers one can multiply (like 3 and 4) to make 12, or the numbers that one can make by multiplying 12 times other numbers. The terms multiple and factor are often confused. What are the multiples of a number?

By example:

Multiples of 3, like …–9, –6, –3, 0, 3, 6, 9, 12, 15… are formed by multiplying 3 by any integer (a “whole” number, negative, zero, or positive, such as…–3, –2, –1, 0, 1, 2, 3…).

Multiples of 12, like …–36, –24, –12, 0, 12, 24, 36, 48, 60…, are all 12 × n, where n is an integer.

Multiples of 2, like …–8, –6, –4, –2, 0, 2, 4, 6, 8, 10, 12…, are all even, 2 × any integer.

Generally:

The multiples of an integer are all the numbers that can be made by multiplying that integer by any integer. Because 21 can be written as 3 × 7, it is a multiple of 3 (and a multiple of 7).

Though 21 can also be written as 2 × 10, it is not generally considered a multiple of 2 (or 10), because the word multiple is generally (always in K–12 mathematics) used only in the context of integers.

• Keeping the concept clear: When naming the multiples of a number, children (and adults!) often forget to include the number, itself, and are often unsure whether or not to include 0. The multiples of 3 include 3 times any integer, including 3 × 0 and 3 × 1. So 3 “is a multiple of 3” (though a trivial one) and 5 “is a multiple of 5” (again, trivial). Zero is a multiple of every number so (among other things) it is an even number. When asked for the “smallest” multiple (for example, the least common multiple), the implication is that only positive multiples are meant. Thus 6 is the “least” common multiple of 3 and 2 even though 0 and –6 (and so on) are also multiples that 3 and 2 have in common, and they are less than 6.
• Keeping the language clear: It is imprecise to refer to a number as “a multiple” without saying what it is a multiple of. The number 12 is “a multiple of 4” or “a multiple of 6” but not just “a multiple.” (It is not, for example, “a multiple” of 5.) Numbers are multiples of something, not just “multiples.”
  Also, 6 is a factor of 12, not a multiple of 12. And 12 is a multiple of 6, not a factor of 6.
• A fine point: The term multiple—like factor and divisible—is generally used only to refer to results of multiplication by a whole number.

Mathematical background

It is often useful to know what multiples two numbers have in common. One way is to list (some of) the multiples of each and look for a pattern. For example, to find the common (positive) multiples of 4 and 6, we might list:

• Multiples of 4:   4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, …
• Multiples of 6:   6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …

The numbers 12, 24, 36, and 48 appear on both of these lists, and more would appear if the lists were longer. They are common multiples, multiples that the two numbers have in common. The least common multiple is the smallest of these: 12. All the other common multiples are multiples of the least common multiple.

Another way of finding the least common multiple of 4 and 6 involves factoring both numbers into their prime factors. The prime factorization of 4 is 2 × 2, and the prime factorization of 6 is 2 × 3. Any common multiple of 4 and 6 will need enough prime factors to make each of these numbers. So, it will need two 2s and one 3—the two 2s that are needed to make 4 (as 2 × 2) and the 3 (along with one of the 2s we already have) to make 6 (as 2 × 3). The prime factorization of this least common multiple is, therefore, 2 × 2 × 3, and the least common multiple is 12.

What’s in a word?

A multiple is what you get by multiplying.

Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200. There are 14 integers that are factors of 400. The biggest factor of 400 is 200. Positive integers that divides 400 without a remainder are listed below.

What are the multiples of 400?

• 1
• 2
• 4
• 5
• 8
• 10
• 16
• 20
• 25
• 40
• 50
• 80
• 100
• 200

What are the factors of 400 in 2 pairs?

• 1 × 400 = 400
• 2 × 200 = 400
• 4 × 100 = 400
• 5 × 80 = 400
• 8 × 50 = 400
• 10 × 40 = 400
• 16 × 25 = 400
• 20 × 20 = 400
• 25 × 16 = 400
• 40 × 10 = 400
• 50 × 8 = 400
• 80 × 5 = 400
• 100 × 4 = 400
• 200 × 2 = 400

FactorFactor Number

1	one
2	two
4	four
5	five
8	eight
10	ten
16	sixteen
20	twenty
25	twenty-five
40	fourty
50	fifty
80	eighty
100	one hundred
200	two hundred

Related Factors

Related Greatest Common Factors of 400

Here are the factors (not including negatives), and some multiples, for 1 to 100:

Factors   Multiples 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

1	2	3	4	5	6	7	8	9	10
1, 2	4	6	8	10	12	14	16	18	20
1, 3	6	9	12	15	18	21	24	27	30
1, 2, 4	8	12	16	20	24	28	32	36	40
1, 5	10	15	20	25	30	35	40	45	50
1, 2, 3, 6	12	18	24	30	36	42	48	54	60
1, 7	14	21	28	35	42	49	56	63	70
1, 2, 4, 8	16	24	32	40	48	56	64	72	80
1, 3, 9	18	27	36	45	54	63	72	81	90
1, 2, 5, 10	20	30	40	50	60	70	80	90	100
1, 11	22	33	44	55	66	77	88	99	110
1, 2, 3, 4, 6, 12	24	36	48	60	72	84	96	108	120
1, 13	26	39	52	65	78	91	104	117	130
1, 2, 7, 14	28	42	56	70	84	98	112	126	140
1, 3, 5, 15	30	45	60	75	90	105	120	135	150
1, 2, 4, 8, 16	32	48	64	80	96	112	128	144	160
1, 17	34	51	68	85	102	119	136	153	170
1, 2, 3, 6, 9, 18	36	54	72	90	108	126	144	162	180
1, 19	38	57	76	95	114	133	152	171	190
1, 2, 4, 5, 10, 20	40	60	80	100	120	140	160	180	200
1, 3, 7, 21	42	63	84	105	126	147	168	189	210
1, 2, 11, 22	44	66	88	110	132	154	176	198	220
1, 23	46	69	92	115	138	161	184	207	230
1, 2, 3, 4, 6, 8, 12, 24	48	72	96	120	144	168	192	216	240
1, 5, 25	50	75	100	125	150	175	200	225	250
1, 2, 13, 26	52	78	104	130	156	182	208	234	260
1, 3, 9, 27	54	81	108	135	162	189	216	243	270
1, 2, 4, 7, 14, 28	56	84	112	140	168	196	224	252	280
1, 29	58	87	116	145	174	203	232	261	290
1, 2, 3, 5, 6, 10, 15, 30	60	90	120	150	180	210	240	270	300
1, 31	62	93	124	155	186	217	248	279	310
1, 2, 4, 8, 16, 32	64	96	128	160	192	224	256	288	320
1, 3, 11, 33	66	99	132	165	198	231	264	297	330
1, 2, 17, 34	68	102	136	170	204	238	272	306	340
1, 5, 7, 35	70	105	140	175	210	245	280	315	350
1, 2, 3, 4, 6, 9, 12, 18, 36	72	108	144	180	216	252	288	324	360
1, 37	74	111	148	185	222	259	296	333	370
1, 2, 19, 38	76	114	152	190	228	266	304	342	380
1, 3, 13, 39	78	117	156	195	234	273	312	351	390
1, 2, 4, 5, 8, 10, 20, 40	80	120	160	200	240	280	320	360	400
1, 41	82	123	164	205	246	287	328	369	410
1, 2, 3, 6, 7, 14, 21, 42	84	126	168	210	252	294	336	378	420
1, 43	86	129	172	215	258	301	344	387	430
1, 2, 4, 11, 22, 44	88	132	176	220	264	308	352	396	440
1, 3, 5, 9, 15, 45	90	135	180	225	270	315	360	405	450
1, 2, 23, 46	92	138	184	230	276	322	368	414	460
1, 47	94	141	188	235	282	329	376	423	470
1, 2, 3, 4, 6, 8, 12, 16, 24, 48	96	144	192	240	288	336	384	432	480
1, 7, 49	98	147	196	245	294	343	392	441	490
1, 2, 5, 10, 25, 50	100	150	200	250	300	350	400	450	500
1, 3, 17, 51	102	153	204	255	306	357	408	459	510
1, 2, 4, 13, 26, 52	104	156	208	260	312	364	416	468	520
1, 53	106	159	212	265	318	371	424	477	530
1, 2, 3, 6, 9, 18, 27, 54	108	162	216	270	324	378	432	486	540
1, 5, 11, 55	110	165	220	275	330	385	440	495	550
1, 2, 4, 7, 8, 14, 28, 56	112	168	224	280	336	392	448	504	560
1, 3, 19, 57	114	171	228	285	342	399	456	513	570
1, 2, 29, 58	116	174	232	290	348	406	464	522	580
1, 59	118	177	236	295	354	413	472	531	590
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60	120	180	240	300	360	420	480	540	600
1, 61	122	183	244	305	366	427	488	549	610
1, 2, 31, 62	124	186	248	310	372	434	496	558	620
1, 3, 7, 9, 21, 63	126	189	252	315	378	441	504	567	630
1, 2, 4, 8, 16, 32, 64	128	192	256	320	384	448	512	576	640
1, 5, 13, 65	130	195	260	325	390	455	520	585	650
1, 2, 3, 6, 11, 22, 33, 66	132	198	264	330	396	462	528	594	660
1, 67	134	201	268	335	402	469	536	603	670
1, 2, 4, 17, 34, 68	136	204	272	340	408	476	544	612	680
1, 3, 23, 69	138	207	276	345	414	483	552	621	690
1, 2, 5, 7, 10, 14, 35, 70	140	210	280	350	420	490	560	630	700
1, 71	142	213	284	355	426	497	568	639	710
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72	144	216	288	360	432	504	576	648	720
1, 73	146	219	292	365	438	511	584	657	730
1, 2, 37, 74	148	222	296	370	444	518	592	666	740
1, 3, 5, 15, 25, 75	150	225	300	375	450	525	600	675	750
1, 2, 4, 19, 38, 76	152	228	304	380	456	532	608	684	760
1, 7, 11, 77	154	231	308	385	462	539	616	693	770
1, 2, 3, 6, 13, 26, 39, 78	156	234	312	390	468	546	624	702	780
1, 79	158	237	316	395	474	553	632	711	790
1, 2, 4, 5, 8, 10, 16, 20, 40, 80	160	240	320	400	480	560	640	720	800
1, 3, 9, 27, 81	162	243	324	405	486	567	648	729	810
1, 2, 41, 82	164	246	328	410	492	574	656	738	820
1, 83	166	249	332	415	498	581	664	747	830
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84	168	252	336	420	504	588	672	756	840
1, 5, 17, 85	170	255	340	425	510	595	680	765	850
1, 2, 43, 86	172	258	344	430	516	602	688	774	860
1, 3, 29, 87	174	261	348	435	522	609	696	783	870
1, 2, 4, 8, 11, 22, 44, 88	176	264	352	440	528	616	704	792	880
1, 89	178	267	356	445	534	623	712	801	890
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90	180	270	360	450	540	630	720	810	900
1, 7, 13, 91	182	273	364	455	546	637	728	819	910
1, 2, 4, 23, 46, 92	184	276	368	460	552	644	736	828	920
1, 3, 31, 93	186	279	372	465	558	651	744	837	930
1, 2, 47, 94	188	282	376	470	564	658	752	846	940
1, 5, 19, 95	190	285	380	475	570	665	760	855	950
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96	192	288	384	480	576	672	768	864	960
1, 97	194	291	388	485	582	679	776	873	970
1, 2, 7, 14, 49, 98	196	294	392	490	588	686	784	882	980
1, 3, 9, 11, 33, 99	198	297	396	495	594	693	792	891	990
1, 2, 4, 5, 10, 20, 25, 50, 100	200	300	400	500	600	700	800	900	1000

See the numbers with only two factors, such as 97? They are prime numbers.

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