Factors of 102 are the numbers which when multiplied in pairs give the product as 102. These factors can be both positive and negative. The number 102 is the first 3-digit number divisible by the numbers 3, 6, 17, 34, and 51. In this lesson, we will calculate the factors of 102, prime factors of 102, and factors of 102 in pairs along with solved examples for a better understanding.

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**Factors of 102:**1, 2, 3, 6, 17, 34, 51 and 102

**Prime Factorization of 102:**102 = 2 × 3 × 17

1. | What Are the Factors of 102? |

2. | How to Calculate Factors of 102? |

3. | Factors of 102 by Prime Factorization |

4. | Factors of 102 in Pairs |

5. | FAQs on Factors of 102 |

## What are the Factors of 102?

Before we study about factors of 102, let"s have a quick recall about "Factor". The number of factors is based on the type of number. A prime number is a number that consists of only two factors. A composite number is a number that has more than two factors. Coming back to number 102. **Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. **Therefore, 102 is a composite number.

To calculate the factors of 102, start with the smallest whole number 1. Divide 102 with the number 1. Is the remainder zero? Yes! By factor definition, the number is divided equally without leaving a remainder.

102 ÷ 1 = 102102 × 1 = 102We try with the next whole number 2. Is the remainder zero? Yes!

102 ÷ 2 = 5151 × 2 = 102Proceeding in a similar manner we get,

102 ÷ 3 = 343 × 34 = 102Hence, the **factors of 102 are 1, 2, 3, 6, 17, 34, 51 and 102.**

**Explore factors using illustrations and interactive examples**

**Important Notes:**

Prime factorization is a process of breaking down the composite number into its prime factors. To get the prime factorization of 102, we divide it by its smallest prime factor, which is 102 ÷ 2 = 51. Now 51 is divided by the prime number 3.

51 ÷ 3 = 17The process of prime factorization continues till we get the quotient as 1. Therefore, factors of 102 by prime factorization are:

It can also be written as 102 = 2 × 3 × 17. 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? And as you might have already guessed, for prime numbers, there are no other factors.

## Factors of 102 in Pairs

Pair factors are the factors of a number given in pairs when multiplied together give that original number. The pair factors of 102 would be the two numbers when multiplied together, result in the value 102. Also, factors of 102 can have negative pair factors as well.

Positive Pair Factors of 102 are:

1 × 102 = 1022 × 51 = 1023 × 34 = 102Positive Pair Factors of 102 are (1, 102), (2, 51) and (3, 34).

Negative Pair Factors of 102 are:

-1 × -102 = 102-2 × -51 = 102-3 × -34 = 102Negative Pair Factors of 102 are (-1, -102), (-2, -51) and (-3, -34).

**Challenging Questions:**

**Example 1: **What will be the sum of all the prime factors of 102?

**Solution:**

We know that the prime factors of 102 = 2, 3, and 17. Thus, the sum of the prime factors = 1 + 3 + 17 = 21. Hence, the sum of the prime factors of 102 is 21.

**Example 2:** Margot is trying to find the maximum number that can divide both 102 and 100. Can we help her?

**Solution:**

A number that divides the given number is a factor of the given number. To solve the given problem, we have to write the factors of each of 102 and 100. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. The factors of 102 are 1, 2, 3, 6, 17, 34, 51, and 102. Thus, the maximum number that can divide both 100 and 102 is 2.

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