# Factors of 102- With Easy Division and Prime Factorization

Contents

**Factors of 102**

**A factor of 102 is a natural number that uniformly divides the original number**. As a result, 102 is divided into two equal parts. These factors are also known as divisors of 102.

Therefore, 102 has more than two factors since it is an even composite number.

**The number 102 is the first even three-digit number.**

If you want to find the factors of 102, we will tell you how to find all the factor of 101.

If you multiply two numbers and the result is 102, they are the factors of 102. Hence, you can represent 102 as a pair factor or as a prime factor.

** In this article, let us discover these factors.**

**How to Find the Factors of 102?**

The factors of 102 can be determined by dividing 102 by the numbers that can evenly divide 102.

102 ÷ 1 = 102

102 ÷ 2 = 51

102 ÷ 3 = 34

102 ÷ 6 = 17

102 ÷ 17 = 6

102 ÷ 34 = 3

102 ÷ 51 = 2

102 ÷ 102 = 1

Therefore, **102 **has eight following factors:

** 1, 2, 3, 6, 17, 34, 51 and 102.**

**What are the Factors of -102?**

We can get -102 by having (-1, 102), (-2, 102), (-3, 102), (-6, 102), (-17, 102), (-34, 102), (-51, 102), (-102, 102) as a pair of factors. Similarly, we can also get -102 by having (1, -102), (2, -102), (3, -102), and (6, -102), (17, -102), (34, -102), (51, -102), (102, -102) as a pair of factors.

**Pair Factors of 102**

Multiplying two factors together results in the original number. As a result, pair factors of 102 would be:

1 × 102 = 102

2 × 51 = 102

3 × 34 = 102

6 × 17 = 102

As a result, the pair **factors of 102 **are **(1, 102), (2, 51), (3, 34), and (6, 17).**

Hence, it is possible to write the negative pair factors as the product of two negative numbers, resulting in 102.

-1 × -102 = 102

-2 × -51 = 102

-3 × -34 = 102

-6 × -17 = 102

Hence, the negative pair factors are **(-1, -102), (-2, -51), (-3, 34) and (-6, 17).**

**Prime Factorization of 102**

By using prime factorization, it is possible to find the prime factors of 102. To find the quotient of 102, divide it by the prime numbers unless the quotient is equal to 1.

102 ÷ 2 = 51 |

51 ÷ 3 = 17 |

17 ÷ 17 = 1 |

Thus, the prime factors are the following:

** 2, 3, and 17.**

Prime factorization of 102 = 2 x 3 x 17Exponential form = 21 x 31 x 171 |

**Solved Examples**

**Q.1: How do you multiply 17 by 102?**

**Solution**: Let n be the number you can multiply that number by 32 to get 102.

So,

** n × 17 = 102**

**n = 102/17**

**n = 6**

Therefore, 6 should be multiplied by 17 to get 102 as the result.

**Q.2: Find the sum of factors of 102. Also, find the factors of the resulting sum.**

**Solution**: 1, 2, 3, 6, 17, 34, 51, and 102 are the factors of the number 102.

Sum of all the factors = **1 + 2 + 3 + 6 + 17 + 34 + 51 + 102**

**Sum = 216**

Therefore, 216 is the required sum.

**Factors of 216 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216**

**Q.2: What is the greatest common factor between 100 and 102?**

**Solution:**

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

The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102

Therefore, 100 and 102 have the following greatest common factor:

**GCF (100, 102) = 2**

**Practice Questions**

- How many divisors does 102 have?
- Calculate the common factors of 102 and 132.
- The GCF of 102 and 136 is?
- Calculate 120 and 102’s GCF.

Link Related Factors | ||

Factors of 30 = 1,2,3,5,6,10,15 and 30. | Factor pair of 24 = 1, 2, 3, 4, 6, 8, 12 and 24. | Prime factorization of 34 = 1,2, 17, and 34. |

Factors of 36 = 1,2,3,4,6,9,12,18, and 36. | Factors of 38= 1, 2, 19, 38. | 41 Factors = 1 and 41. |

Factors of 45 = 1, 3, 5, 9, 15, and 45. | Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. | 103 Factors = 1 and 103. |

Factors of 50 = 1, 2, 5, 10, 25, 50. | Factors of 54 = 1, 2, 3, 6, 9, 18, 27 and 54. | Factors of 56 = 1, 2, 4, 7, 8, 14, 28 and 56. |

**FAQ`S**

**What are the factors of 102?**

102 has the following factors:**1, 2, 4, 8, 16, 32, 64, and 102.**

**How many ways can you make 102?**

Two numbers can be combined to form 102, in four different ways:**1 x 102****2 x 51****3 x 34****6 x 17**

**What is the 5th multiple of 102?**

510 is the fifth multiple of 102.

**What is the prime factor form of 102?**

**2 x 3 x 17** is the prime factor form of 102

**Is 102 a perfect cube?**

There is no perfect cube in 102. So,102 is a cube with no natural numbers.

**Is 102 a composite number or a prime number?**

Since it has more than two factors, 102 is a composite number.