Divisibility Rule of 117

The divisibility rule for 117 is a method by which we can find out if a number is divisible by 117 or not without using the division method. Check whether 4095 is divisible by 117 with the divisibility rule.

Step 1: Break down the number 117 into its prime factors: 117 = 3 × 39.  

Step 2: Check the divisibility of the number for each of the factors.  
- For 3: Add all the digits of the number. If the sum is a multiple of 3, then the number is divisible by 3. For 4095, 4 + 0 + 9 + 5 = 18, and 18 is a multiple of 3.  
- For 39: Check if the number is divisible by 39 using either direct division or by applying divisibility rules for 3 and 13, since 39 = 3 × 13.  

Step 3: If the number is divisible by both 3 and 39, then it is divisible by 117. Since 4095 satisfies these conditions, it is divisible by 117.

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 117.

Know the multiples of 117:

Memorize the multiples of 117 (117, 234, 351, 468, etc.) to quickly check divisibility. If a number is a multiple of 117, then it is divisible by 117.

Use prime factorization:

By understanding the prime factorization of 117, you can apply known divisibility rules for smaller factors like 3 and 39 to simplify the process.

Repeat the process for large numbers:

For large numbers, continue checking divisibility by breaking down into smaller factors until you reach a number divisible by 117.

Use the division method to verify:

Students can use the division method as a way to verify and crosscheck their results, ensuring they have applied the rule correctly.

• Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.

• Prime factorization: The expression of a number as the product of its prime factors.

• Multiples: The results we get after multiplying a number by an integer.

• Integers: The numbers that include all the whole numbers, negative numbers, and zero.

• Subtraction: The process of finding the difference between two numbers by reducing one number from another.