Factors of 102

The numbers that divide 102 evenly are known as factors of 102. A factor of 102 is a number that divides the number without remainder. The factors of 102 are 1, 2, 3, 6, 17, 34, 51, and 102.

Negative factors of 102: -1, -2, -3, -6, -17, -34, -51, and -102.

Prime factors of 102: 2, 3, and 17.

Prime factorization of 102: 2 × 3 × 17.

The sum of factors of 102: 1 + 2 + 3 + 6 + 17 + 34 + 51 + 102 = 216

Factors can be found using different methods. Mentioned below are some commonly used methods:

1. Finding factors using multiplication
2. Finding factors using division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 102. Identifying the numbers which are multiplied to get the number 102 is the multiplication method.

Step 1: Multiply 102 by 1, 102 × 1 = 102.

Step 2: Check for other numbers that give 102 after multiplying 2 × 51 = 102

3 × 34 = 102

6 × 17 = 102

Therefore, the positive factor pairs of 102 are: (1, 102), (2, 51), (3, 34), and (6, 17). For every positive factor, there is a negative factor.

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following the simple division method -

Step 1: Divide 102 by 1, 102 ÷ 1 = 102.

Step 2: Continue dividing 102 by the numbers until the remainder becomes 0.

102 ÷ 1 = 102

102 ÷ 2 = 51

102 ÷ 3 = 34

102 ÷ 6 = 17

Therefore, the factors of 102 are: 1, 2, 3, 6, 17, 34, 51, 102.

The factors can be found by dividing it with a prime number. We can find the prime factors using the following methods:

• Using prime factorization
• Using factor tree

Using Prime Factorization: In this process, prime factors of 102 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

102 ÷ 2 = 51

51 ÷ 3 = 17

17 ÷ 17 = 1

The prime factors of 102 are 2, 3, and 17. The prime factorization of 102 is: 2 × 3 × 17.

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 102 is divided by 2 to get 51.

Step 2: Now divide 51 by 3 to get 17.

Step 3: Here, 17 is a prime number and cannot be divided anymore. So, the prime factorization of 102 is: 2 × 3 × 17.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs

• Positive factor pairs of 102: (1, 102), (2, 51), (3, 34), and (6, 17).
• Negative factor pairs of 102: (-1, -102), (-2, -51), (-3, -34), and (-6, -17).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 102 are 1, 2, 3, 6, 17, 34, 51, and 102.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 17 are prime factors of 102.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 102 are (1, 102), (2, 51), etc.

• Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 102 is 2 × 3 × 17.

• Negative factors: Factors that are negative integers. For example, -1, -2, -3, etc., are negative factors of 102.