In number theory, a factor of a natural number (positive integer) is an integer that divides evenly into that original number. In simple terms, a factor of a number will leave no remainder when divided. Here, the factor of 100 is the integer that results in 100 when multiplied together. Factor pairs of 100 consist of whole numbers that can be positive or negative, but not fractions or decimals. To find the factors of 100, we will learn about various methods like the division method and prime factorization and also find the pairs of 100.

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## What are the Factors of 100?

The factors of 100 are the integers that can be multiplied together to produce 100. Since 100 is an even composite number, it has multiple factors in addition to 1 and itself. The factors of 100 consist of positive and negative numbers that can be evenly divided into 100. The term “hundred” was first coined in the year 1920 by nine-year-old Milton Sirotta, who was the nephew of the U.S. mathematician Edward Kasner.

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

**Also Read – ****Factors of 27: Sum, Negative 27, Factor Pairs**

## Way to Calculate the Factors of 100

To calculate the factors of 100, we need to start from the smallest whole number, which is 1 and so on. Let us calculate and see if the remainder is 0.

- 100 ÷ 1 = 100
- 100 × 1 = 100
- 100 ÷ 2 = 50
- 50 × 2 = 100

Hence, we further divide and multiply the digits we get –

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

## Factors of 100 by Divison Method

The factors of 100 can also be calculated by the simplest method of division. In this method, the number i.e 100 is divided by different consecutive numbers. If the integers do not leave a remainder and are exactly divided by 100, then the number is the factor of 100 and so on. Let us see in steps –

- 100 ÷ 1 = 100 Here the factor is 1 with no remainder
- 100 ÷ 2 = 50 Factor – 2, Remainder – 0
- 100 ÷ 4 = 25 Factor – 4 and no remainder
- 100 ÷ 5 =20 Factor – 5, Remainder – 0
- 100 ÷ 10 = 10 Factor – 10, Remainder – 0
- 100 ÷ 20 = 5 Factor – 20, Remainder – 0
- 100 ÷ 25 = 4 Factor – 10, Remainder – 0
- 100 ÷ 50 = 2 Factor – 50, Remainder – 0
- 100 ÷100 = 1 Here, the factor is 100 itself and no remainder.

The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. When we divide 100 by any other numbers, it leaves a remainder which tells us that those numbers are not factors of 100.

Like for example –

- 100 ÷ 3 = 33.333 Factor – 3, Remainder – 33.333
- 100 ÷ 6 =16.667 Factor – 6, Remainder – 16.67
- 100 ÷ 7 =14.286 Factor – 7, Remainder – 14.29
- 100 ÷ 8 =12.5 Factor – 8, Remainder – 12.5
- 100 ÷ 9 =11.111 Factor – 9, Remainder – 11.11
- 100 ÷ 11 =9.091 Factor – 11, Remainder – 9.091

**Also Read – ****Factors of 11: Sum, Negative Factors, Factor Pairs and more!**

## Prime Factorization of 100

**Prime factorization** is a way of breaking down a whole number into a product of its prime factors. Let us get to know the factors of 100 by this method –

- Step – 1: When we divide 100 by the smallest prime number i.e. 2. We get – 100 divided by 2 equals 50 with no remainder (100 / 2 = 50), Hence, 2 is a prime factor of 100.
- Step – 2: Now, we are left with 50. Now, we can again divide by 2, resulting in 25 (50 / 2 = 25). This confirms that 2 is a factor present twice in the prime factorization (2 x 2).
- Step-3: We are now working with 25. This can be further broken down as 5 x 5, where 5 is another prime number.

We can also simply understand it by a factor tree of 100.

100

/ \

2 50

/ \

2 25

/ \

5 5

- Therefore, expressing 100 in terms of its prime factors, we get 100 = 2 x 2 x 5 x 5.

## Factors Pairs of 100

A factor pair of a number consists of two individual factors that so when multiplied together, they result in the original number. Hence to find the factors of 100 pairs, we have to multiply the numbers in pairs to get 100. These can be found by positive factor pair and negative factor pair –

Example of a positive factor pair of a factor of 100 –

1 × 100 = 100 | (1, 100) |

Multiplication of 100 | Positive Pair factor |

2 × 50 = 100 | (2, 50) |

4 × 25 = 100 | (4, 25) |

5 × 20 = 100 | (5, 20) |

10 × 10 = 100 | (10, 10) |

20 × 5 = 100 | (20, 5) |

25 × 4 = 100 | (25, 4) |

50 × 2 = 100 | (50, 2) |

100 × 1 = 100 | (100, 1) |

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

Example of a negative factor pair of a factor of 100 –

-1 × -100 = 100 | (-1, -100) |

-2 × – 50 = 100 | (-2, -50) |

Multiplication of 100 | Negative Pair factor |

-4 × -25 = 100 | (-4,-25) |

-5 × -20 = 100 | (-5, -20) |

-10 × -10 = 100 | (-10, -10) |

-20 × -5 = 100 | (-20, -5) |

-25 × -4 = 100 | (-25, -4) |

-50 × -2 = 100 | (-50, -2) |

-100 × -1 = 100 | (-100, -1) |

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

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