Divisibility Rule of 975

The divisibility rule for 975 is a method by which we can determine if a number is divisible by 975 without using the division method. To apply this rule, a number must be divisible by 3, 5, and 13 (since 975 = 3 × 5 × 13).

Example: Check whether 2925 is divisible by 975.

Step 1: Check divisibility by 3. A number is divisible by 3 if the sum of its digits is divisible by 3. For 2925: 2 + 9 + 2 + 5 = 18, which is divisible by 3.

Step 2: Check divisibility by 5. A number is divisible by 5 if it ends in 0 or 5. 2925 ends in 5, so it is divisible by 5.

Step 3: Check divisibility by 13. A number is divisible by 13 if you can subtract 9 times the last digit from the rest of the number and get a result divisible by 13. For 2925: Subtract 9 times 5 (last digit) from 292: 292 - 45 = 247, and 247 is divisible by 13.

Since 2925 is divisible by 3, 5, and 13, it is divisible by 975.
 

Learning the divisibility rule will help kids to master division. Here are a few tips and tricks for the divisibility rule of 975:

Know the prime factors:

Understand the prime factors of 975 (3, 5, and 13) and use their individual divisibility rules.

Use divisibility shortcuts:

Familiarize yourself with the divisibility rules for 3, 5, and 13 to quickly check each criterion.

Repeat the process for large numbers:

For large numbers, apply the divisibility rules sequentially for each factor of 975.

Use the division method to verify:

Verify your results using the division method to cross-check and confirm comprehension.

• Divisibility rule: The set of rules used to find out whether a number is divisible by another number.

• Prime factors: The prime numbers that multiply together to give a number (for 975, they are 3, 5, and 13).

• Multiple: A multiple is the result of multiplying a number by an integer.

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

• Integer: Whole numbers, including negative numbers and zero.