# Factors of 100

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

#### How to find factors of a number

 1.   Find factors of 100 using Division Method 2.   Find factors of 100 using Prime Factorization 3.   Find factors of 100 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 100

• Divide 100 by 1: 100 ÷ 1 : Remainder = 0
• Divide 100 by 2: 100 ÷ 2 : Remainder = 0
• Divide 100 by 4: 100 ÷ 4 : Remainder = 0
• Divide 100 by 5: 100 ÷ 5 : Remainder = 0
• Divide 100 by 10: 100 ÷ 10 : Remainder = 0
• Divide 100 by 20: 100 ÷ 20 : Remainder = 0
• Divide 100 by 25: 100 ÷ 25 : Remainder = 0
• Divide 100 by 50: 100 ÷ 50 : Remainder = 0
• Divide 100 by 100: 100 ÷ 100 : Remainder = 0

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

#### 2. Steps to find factors of 100 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 100 using the division method, follow these steps:

• Step 1. Start dividing 100 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 100, which is 2. Divide 100 by 2 to obtain the quotient (50).
100 ÷ 2 = 50
• Step 3. Repeat step 1 with the obtained quotient (50).
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

So, the prime factorization of 100 is, 100 = 2 x 2 x 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 100 as shown below:

So, the prime factorization of 100 is, 100 = 2 x 2 x 5 x 5.

#### 3. Find factors of 100 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 100 would be the two numbers which, when multiplied, give 100 as the result.

The following table represents the calculation of factors of 100 in pairs:

Factor Pair Pair Factorization
1 and 100 1 x 100 = 100
2 and 50 2 x 50 = 100
4 and 25 4 x 25 = 100
5 and 20 5 x 20 = 100
10 and 10 10 x 10 = 100

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 100. They are called negative pair factors.

Hence, the negative pairs of 100 would be ( -1 , -100 ) , ( -2 , -50 ) , ( -4 , -25 ) , ( -5 , -20 ) and ( -10 , -10 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 100 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 100.
• Every number is a factor of zero (0), since 100 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 4, 5, 10, 20, 25, 50, 100 are exact divisors of 100.
• Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. Each factor divides 100 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 10, 20, 25, 50, 100 are all less than or equal to 100.

• What are the prime factors of 100?

The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100.
Prime factors of 100 are 2, 2, 5, 5.

• What is the sum of all factors of 100?

The sum of all factors of 100 is 217.

• What are the pair factors of 100?

Pair factors of 100 are (1,100), (2,50), (4,25), (5,20), (10,10).

• What two numbers make 100?

Two numbers that make 100 are 2 and 50.

• What are multiples of 100?

First five multiples of 100 are 200, 300, 400, 500.

• Is 100 a perfect square?

Yes 100 is a perfect square.

• Which is greatest factor of 100?

The greatest factor of 100 is 50.

• How do you factors of 100?

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

• What are five multiples of 100?

First five multiples of 100 are 200, 300, 400, 500, 600.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 100?

Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100.
Even factors of 100 are 2, 4, 10, 20, 50, 100.
Hence, product of even factors of 100 is; 2 x 4 x 10 x 20 x 50 x 100 = 8000000.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 100? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 10, 20, 25, 50, 100.
Negative factors are -1, -2, -4, -5, -10, -20, -25, -50, -100.

How many factors are there for 100?

Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100.
So there are in total 9 factors.

Sammy is puzzled while calculating the prime factors of 100. Can you help him find them?

Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100.
Prime factors of 100 are 2, 2, 5, 5

Joey wants to write all the prime factors of 100 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 100 are 2, 2, 5, 5.
So in exponential form it can be written as 22 x 52.

What is prime factorization of 100?

Prime factorization of 100 is 2 x 2 x 5 x 5 = 22 x 52.

Can you help Rubel to find out the product of the even factors of 100?

Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100.
Even factors of 100 are 2, 4, 10, 20, 50, 100.
Hence, product of even factors of 100 is; 2 x 4 x 10 x 20 x 50 x 100 = 8000000.