What are the Factors of 117?
If we divide 117 by a number and it leaves 0 as the remainder, the number will be the factor of 117. In simple words, the numbers that are multiplied together in pairs resulting in the number 117 are the factors of 117. If we divide 117 by a number and that results in a remainder that is other than 0, the number will not be a factor of 117.
The factors of 117 are 1, 3, 9, 13, 39 and 117. There are only 6 factors of 117. No other positive integer can divide 117 completely.
Divisibility Rule to Find the Factors of 117
Divisor | Is the number a factor of 117? | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of every number. | 1 x 117 = 117 |
2 | No, 117 is not even. | - |
3 | Yes, 1 + 1 + 7 = 9 is divisible by 3. | 3 x 39 = 117 |
4 | No, as 117 \(\div\) 4 = 29 and the remainder = 1. | - |
5 | No, the ones digit is neither 0 nor 5. | - |
6 | No, 117 is not even. | - |
7 | No, as 117 \(\div\) 7 = 16 and the remainder = 5. | - |
8 | No, as 117 \(\div\) 8 = 14 and the remainder = 5. | - |
9 | Yes, 117 \(\div\) 9 = 13 and the remainder = 0. | 13 x 9 = 117 |
Factors of 117 by the Division Method
If we divide 117 by 1, we get 117 and 0 as the quotient and the remainder, respectively. So, 1 is the factor of 117.
If we divide 117 by 3, we get 39 and 0 as the quotient and the remainder, respectively. So, 3 is the factor of 117.
If we divide 117 by 9, we get 13 and 0 as the quotient and the remainder, respectively. So, 9 is the factor of 117.
If we divide 117 by 13, we get 9 and 0 as the quotient and the remainder, respectively. So, 13 is the factor of 117.
If we divide 117 by 39, we get 3 and 0 as the quotient and the remainder, respectively. So, 39 is the factor of 117.
If we divide 117 by 117, we get 1 and 0 as the quotient and the remainder, respectively. So, 117 is the factor of 117.
Prime Factorization of 117
A natural number can be obtained by multiplying some prime numbers. These prime numbers are known as the prime factors of that natural number. The process of representing a number as a product of its prime factors is known as prime factorization.
Since 117 is a composite number having composite factors, we can further divide those composite factors to get prime factors. The prime factorization of 117 can be represented using a factor tree as illustrated below:
So, the prime factorization of 117 is 117 = 3 x 3 x 13 or \(3^2\) x 13.
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Factor Pairs of 117
The factor pairs of 117 are the pairs of numbers whose multiplication is 117. The factors of 117 are:
1 x 117 = 117
3 x 39 = 117
9 x 13 = 117
We can also write the factor pairs in ordered pairs: (1, 117), (3, 39) and (9, 13).
Rapid Recall
Solved Factors of 117 Examples
Example 1: Find the common factor of 46 and 117.
Solution:
The factors of 46 = 1, 2, 23 and 46.
The factors of 117 = 1, 3, 9, 13, 39 and 117.
Therefore, the common factor of 46 and 117 is 1.
Example 2: Find the greatest common factor of 65 and 117.
Solution:
The factors of 65 = 1, 5, 13 and 65.
The factors of 117 = 1, 3, 9, 13, 39 and 117.
The common factors of 65 and 117 are 1 and 13.
Therefore, the greatest common factor of 65 and 117 is 13.
Example 3: Sid and his friend Tom are solving a riddle. The final piece of information gives them a secret two-digit code to open the treasure box. The final step says, “To open the lock, find the product of the prime factors of 117.” What is the two-digit secret code?
Solution:
The prime factors of 117 are 3 and 13.
The product of the prime factors = 3 × 1 3
= 39.
So, the secret code to open the treasure box is 39.
Example 4: Is 117 completely divisible by 3?
Solution:
Yes, 1 + 1 + 7 = 9. Therefore, it is divisible by 3.
So, when we divide 117 by 3, we get 39 as the quotient and 0 as the remainder, respectively.
The factors of 117 are the numbers that divide 117 exactly, leaving 0 as the remainder. 117 is completely divisible by 1, 3, 9, 13, 39 and 117 only. So, the factors of 117 are 1, 3, 9, 13, 39 and 117.
The factors of 117 are 1, 3, 9, 13, 39 and 117.
The sum of the factors = 1 + 3 + 9 + 13 + 39 + 117 = 182.
The factors of 117 are 1, 3, 9, 13, 39 and 117.
The product of the factors = 1 x 3 x 9 x 13 x 39 x 117 = 1601613.
Yes, 117 is a composite number as it has factors other than one and itself. It has the factors 3, 9, 13 and 39 other than 1 and 117.