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

#### Related Greatest Common Factors of 400

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

Factors   Multiples
11 2345678910
1, 22 468101214161820
1, 33 6912151821242730
1, 2, 44 81216202428323640
1, 55 101520253035404550
1, 2, 3, 66 121824303642485460
1, 77 142128354249566370
1, 2, 4, 88 162432404856647280
1, 3, 99 182736455463728190
1, 2, 5, 1010 2030405060708090100
1, 1111 2233445566778899110
1, 2, 3, 4, 6, 1212 24364860728496108120
1, 1313 263952657891104117130
1, 2, 7, 1414 284256708498112126140
1, 3, 5, 1515 3045607590105120135150
1, 2, 4, 8, 1616 3248648096112128144160
1, 1717 34516885102119136153170
1, 2, 3, 6, 9, 1818 36547290108126144162180
1, 1919 38577695114133152171190
1, 2, 4, 5, 10, 2020 406080100120140160180200
1, 3, 7, 2121 426384105126147168189210
1, 2, 11, 2222 446688110132154176198220
1, 2323 466992115138161184207230
1, 2, 3, 4, 6, 8, 12, 2424 487296120144168192216240
1, 5, 2525 5075100125150175200225250
1, 2, 13, 2626 5278104130156182208234260
1, 3, 9, 2727 5481108135162189216243270
1, 2, 4, 7, 14, 2828 5684112140168196224252280
1, 2929 5887116145174203232261290
1, 2, 3, 5, 6, 10, 15, 3030 6090120150180210240270300
1, 3131 6293124155186217248279310
1, 2, 4, 8, 16, 3232 6496128160192224256288320
1, 3, 11, 3333 6699132165198231264297330
1, 2, 17, 3434 68102136170204238272306340
1, 5, 7, 3535 70105140175210245280315350
1, 2, 3, 4, 6, 9, 12, 18, 3636 72108144180216252288324360
1, 3737 74111148185222259296333370
1, 2, 19, 3838 76114152190228266304342380
1, 3, 13, 3939 78117156195234273312351390
1, 2, 4, 5, 8, 10, 20, 4040 80120160200240280320360400
1, 4141 82123164205246287328369410
1, 2, 3, 6, 7, 14, 21, 4242 84126168210252294336378420
1, 4343 86129172215258301344387430
1, 2, 4, 11, 22, 4444 88132176220264308352396440
1, 3, 5, 9, 15, 4545 90135180225270315360405450
1, 2, 23, 4646 92138184230276322368414460
1, 4747 94141188235282329376423470
1, 2, 3, 4, 6, 8, 12, 16, 24, 4848 96144192240288336384432480
1, 7, 4949 98147196245294343392441490
1, 2, 5, 10, 25, 5050 100150200250300350400450500
1, 3, 17, 5151 102153204255306357408459510
1, 2, 4, 13, 26, 5252 104156208260312364416468520
1, 5353 106159212265318371424477530
1, 2, 3, 6, 9, 18, 27, 5454 108162216270324378432486540
1, 5, 11, 5555 110165220275330385440495550
1, 2, 4, 7, 8, 14, 28, 5656 112168224280336392448504560
1, 3, 19, 5757 114171228285342399456513570
1, 2, 29, 5858 116174232290348406464522580
1, 5959 118177236295354413472531590
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 6060 120180240300360420480540600
1, 6161 122183244305366427488549610
1, 2, 31, 6262 124186248310372434496558620
1, 3, 7, 9, 21, 6363 126189252315378441504567630
1, 2, 4, 8, 16, 32, 6464 128192256320384448512576640
1, 5, 13, 6565 130195260325390455520585650
1, 2, 3, 6, 11, 22, 33, 6666 132198264330396462528594660
1, 6767 134201268335402469536603670
1, 2, 4, 17, 34, 6868 136204272340408476544612680
1, 3, 23, 6969 138207276345414483552621690
1, 2, 5, 7, 10, 14, 35, 7070 140210280350420490560630700
1, 7171 142213284355426497568639710
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 7272 144216288360432504576648720
1, 7373 146219292365438511584657730
1, 2, 37, 7474 148222296370444518592666740
1, 3, 5, 15, 25, 7575 150225300375450525600675750
1, 2, 4, 19, 38, 7676 152228304380456532608684760
1, 7, 11, 7777 154231308385462539616693770
1, 2, 3, 6, 13, 26, 39, 7878 156234312390468546624702780
1, 7979 158237316395474553632711790
1, 2, 4, 5, 8, 10, 16, 20, 40, 8080 160240320400480560640720800
1, 3, 9, 27, 8181 162243324405486567648729810
1, 2, 41, 8282 164246328410492574656738820
1, 8383 166249332415498581664747830
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 8484 168252336420504588672756840
1, 5, 17, 8585 170255340425510595680765850
1, 2, 43, 8686 172258344430516602688774860
1, 3, 29, 8787 174261348435522609696783870
1, 2, 4, 8, 11, 22, 44, 8888 176264352440528616704792880
1, 8989 178267356445534623712801890
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 9090 180270360450540630720810900
1, 7, 13, 9191 182273364455546637728819910
1, 2, 4, 23, 46, 9292 184276368460552644736828920
1, 3, 31, 9393 186279372465558651744837930
1, 2, 47, 9494 188282376470564658752846940
1, 5, 19, 9595 190285380475570665760855950
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 9696 192288384480576672768864960
1, 9797 194291388485582679776873970
1, 2, 7, 14, 49, 9898 196294392490588686784882980
1, 3, 9, 11, 33, 9999 198297396495594693792891990
1, 2, 4, 5, 10, 20, 25, 50, 100100 2003004005006007008009001000

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