What is the sum of the prime factors of 100

Use this prime numbers calculator to find all prime factors of a given integer number up to 10 trillion. This calculator presents:

1. Prime factors of a number
2. Prime decomposition in exponential form
3. CSV (comma separated values) list of prime factors
4. Factorization in a prime factors tree

For the first 5000 prime numbers, this calculator indicates the index of the prime number. The nth prime number is denoted as Prime[n], so Prime[1] = 2, Prime[2] = 3, Prime[3] = 5, and so on.

The limit on the input number to factor is less than 10,000,000,000,000 (less than 10 trillion or a maximum of 13 digits).

What is Prime Factorization?

Prime factorization or integer factorization of a number is breaking a number down into the set of prime numbers which multiply together to result in the original number. This is also known as prime decomposition.

How to Find Prime Factorization of a Number

We cover two methods of prime factorization: find primes by trial division, and use primes to create a prime factors tree.

Prime Factorization by Trial Division

Say you want to find the prime factors of 100 using trial division. Start by testing each integer to see if and how often it divides 100 and the subsequent quotients evenly. The resulting set of factors will be prime since, for example, when 2 is exhausted all multiples of 2 are also exhausted.

Find the prime factors of 100:

• 100 ÷ 2 = 50; save 2
• 50 ÷ 2 = 25; save 2
• 25 ÷ 2 = 12.5, not evenly so divide by next highest number, 3
• 25 ÷ 3 = 8.333, not evenly so divide by next highest number, 4
• But, 4 is a multiple of 2 so it has already been checked, so divide by next highest number, 5
• 25 ÷ 5 = 5; save 5
• 5 ÷ 5 = 1; save 5

List the resulting prime factors as a sequence of multiples, 2 x 2 x 5 x 5 or as factors with exponents, 22 x 52.

Examples of Prime Decomposition: Factors and Exponents

• Prime factorization of 100 is 2 x 2 x 5 x 5 or 22 x 52
• Prime factorization of 76 is 2 x 2 x 19 or 22 x 191
• Prime factorization of 50 is 2 x 5 x 5 or 2 x 52
• Prime factorization of 48 is 2 x 2 x 2 x 2 x 3 or 24 x 31
• Prime factorization of 36 is 2 x 2 x 3 x 3 or 22 x 32
• Prime factorization of 20 is 2 x 2 x 5 or 22 x 51
• Prime factorization of 10 is 2 x 5 or 21 x 51

Prime Factors Tree

Using a prime factorization tree to see the work, prime decomposition of 100 = 2 x 2 x 5 x 5 looks like this:

Related Calculators

For a list of the first 1000 prime numbers see our See 1000 Prime Numbers Table.

References and Further Reading

Math is Fun: Prime Factorization.

Weisstein, Eric W. "Prime Number." From MathWorld--A Wolfram Web Resource.

Weisstein, Eric W. "Direct Search Factorization." From MathWorld--A Wolfram Web Resource.

Weisstein, Eric W. "Prime Factorization Algorithms." From MathWorld--A Wolfram Web Resource.

Caldwell, Chris K. The Prime Pages.

Factors of 100 are the collection of both positive and negative numbers which can be evenly divided into 100. The word hundred was invented in 1920 by nine-year-old Milton Sirotta (1911-1981), nephew of Edward Kasner, a U.S. mathematician. Learning about the factors of 100 is useful in learning advanced Maths concepts. In this lesson, we will calculate the factors of 100, its prime factors, its factors in pairs, and we will finish by solving some examples for better understanding.

• Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, and 100
• Factors of -100: -1, -2, -4, -5, -10, -20, -25, -50 and -100
• Prime Factorization of 100: 100 = 22 × 52

What are Factors of 100?

The factors of 100 are all the integers 100 can be divided into. The number 100 is an even composite number.

As it is even, it will have 2 as its factor. To understand why it is composite, let's recall the definition of a composite number. A number having a total count of factors in excess of two is defined as a composite number. On the other hand, a number such as 17 is a prime number because it has only 2 factors i.e. 1 and 17.

Now accordingly the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

How to Calculate the Factors of 100?

Let's begin calculating the factors of 100, starting with the smallest whole number, i.e., 1. Divide 100 with this number. Is the remainder 0? Yes! So, we will get:

• 100 ÷ 1 = 100
• 100 × 1 = 100

The next whole number is 2. Now divide 100 with this number:

• 100 ÷ 2 = 50
• 2 × 50 = 100

Proceeding in a similar manner, we get other numbers 100 can be divided by. They can be written as:

• 1 × 100 = 100
• 2 × 50 = 100
• 4 × 25 = 100
• 5 × 20 = 100
• 10 × 10 = 100

Explore factors using illustrations and interactive examples:

• Factors of 175 - The factors of 175 are 1, 5, 7, 25, 35, 175
• Factors of 15 - The factors of 15 are 1, 3, 5, 15
• Factors of 25 - The factors of 25 are 1, 5, 25
• Factors of 35 - The factors of 35 are 1, 5, 7, 35
• Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21, 63
• Factors of 54 - The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

Factors of 100 by Prime Factorization

Prime factorization means expressing a composite number as the product of its prime factors.

• Step 1: To get the prime factorization of 100, we divide it by its smallest prime factor, 2 like 100 ÷ 2 = 50.
• Step 2: Now, 50 is divided by its smallest prime factor, and the quotient is obtained.
• Step 3: This process goes on till we get the quotient as 1.
• The prime factorization of 100 in the form of a factor tree is shown below.

The above factorization is the tree diagram representation of factors of 100. Therefore, factors of 100 = 2 × 2 × 5 × 5

Q: Now that we have done the prime factorization of our number, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not?

A: And as you might have already guessed, for prime numbers, there are no other factors.

Factors of 100 in Pairs

The pair, consisting of numbers that give 100 when multiplied, is known as the factor pair of 100. The following are the factors of 100 in pairs:

Observe in the table above, after 10 × 10, the factors start repeating. So, it is enough to find factors until (10,10). If we consider negative integers, then both the numbers in the pair factors will be negative i.e. - ve (×) - ve = + ve.

So, we can have negative factor pairs of 100 as (-1,-100), (-2,-50), (-4,-25), (-5,-20), and (-10,-10).

Important Notes:

• The numbers which we multiply to get 100 are the factors of 100.
• Factors of 100 are written as 1, 2, 4, 5, 10, 20, 25, 50, and 100.
• Factor pairs are the pairs of two numbers that, when multiplied, give the original number. The pair factor of 100 are (1,100), (2,50), (4,25), (5,20), and (10,10).

1. Example 1: Help Alastair list the factors of 100 and find the factor pairs.

   Solution:

   Factors of 100 are the numbers that divide 100 without any remainder. They are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Factors pairs are the pairs of two numbers that, when multiplied, give 100:

   1 × 100 = 100

   2 × 50 = 100

   4 × 25 = 100

   5 × 20 = 100

   10 × 10 = 100

   Hence, pairs of 100 are (1, 100), (2, 50), (4, 25), (5, 20), and (10, 10).

2. Example 2: Kevin has to list the factors of 100 and factors of 200 and find the common factors between them. Can you help him do it?

   Solution:

   Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100 and the factors of 200 are 1, 2, 4, 5, 10, 20, 25, 40, 50, 100, and 200. We can see that 1, 2, 4, 5, 10, 20, 25, 50, and 100 are the common factors of 100 and 200.

   Hence, common factors of 100 and 200 are 1, 2, 4, 5,10, 20, 25, 50, and 100.

3. Example 3: Alina's mother promised to give her 3 chocolate cookies if she is able to list all the factors of 100. Can you help Alina list the factors of 100?

   Solution:

   Factors of 100 are numbers that divide 100 exactly without any remainder.

   100 ÷ 1 = 100

   100 ÷ 2 = 50

   100 ÷ 4 = 25

   100 ÷ 5 = 20

   100 ÷ 10 = 10

   Hence, factors of 100 are 1, 2, 4, 5,10, 20, 25, 50, and 100.

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FAQs on Factors of 100

What are Factor Pairs of 100?

The factor pairs of 100 are (1, 100), (2, 50), (4, 25), (5, 20), and (10, 10).

What are the Factors of 100 and 75?

The factors of 100 are 100, 50, 25, 20, 10, 5, 4, 2, and 1. Similarly, factors of 75 are 1, 3, 5, 15, 25, and 75.
Therefore, the common factors of 100 and 75 are 1, 5, and 25.

What are the Negative Factors of 100?

Negative factors of 100 are written as -1, -2, -4, -5, -10, -20, -25, -50, and -100.

What are Common Factors of 100 and 25?

Factors of 100 are written as 1, 2, 4, 5, 10, 20, 25, 50, and 100 and the factors of 25 are 1, 5, and 25.
Hence, Common factors of 100 and 25 are 1, 5, and 25.

What are the Factors of 100?

Factors of 100 are written as 1, 2, 4, 5, 10, 20, 25, 50, and 100.