Factors of 117

The numbers that divide 117 evenly are known as factors of 117. A factor of 117 is a number that divides the number without remainder. The factors of 117 are 1, 3, 9, 13, 39, and 117.

Negative factors of 117: -1, -3, -9, -13, -39, and -117.

Prime factors of 117: 3 and 13.

Prime factorization of 117: 3² × 13.

The sum of factors of 117: 1 + 3 + 9 + 13 + 39 + 117 = 182

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 117. Identifying the numbers which are multiplied to get the number 117 is the multiplication method.

Step 1: Multiply 117 by 1, 117 × 1 = 117.

Step 2: Check for other numbers that give 117 after multiplying 3 × 39 = 117 9 × 13 = 117

Therefore, the positive factor pairs of 117 are: (1, 117), (3, 39), (9, 13).

All these factor pairs result in 117. 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 a simple division method -

Step 1: Divide 117 by 1, 117 ÷ 1 = 117.

Step 2: Continue dividing 117 by the numbers until the remainder becomes 0.

117 ÷ 1 = 117

117 ÷ 3 = 39

117 ÷ 9 = 13

Therefore, the factors of 117 are: 1, 3, 9, 13, 39, 117.

The factors can be found by dividing it with prime numbers. 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 117 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

117 ÷ 3 = 39

39 ÷ 3 = 13

13 ÷ 13 = 1

The prime factors of 117 are 3 and 13. The prime factorization of 117 is: 3² × 13.

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

Step 1: Firstly, 117 is divided by 3 to get 39.

Step 2: Now divide 39 by 3 to get 13. Here, 13 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 117 is: 3² × 13.

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 117: (1, 117), (3, 39), (9, 13).
• Negative factor pairs of 117: (-1, -117), (-3, -39), (-9, -13).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 117 are 1, 3, 9, 13, 39, and 117.

• Prime factors: The factors which are prime numbers. For example, 3 and 13 are prime factors of 117.

• 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 117 are (1, 117), (3, 39), etc.

• Multiplication method: A way to find factors by identifying pairs of numbers that multiply to the target number.

• Prime factorization: The process of expressing a number as a product of its prime factors. For example, 117 = 3² × 13.