Divisibility Rule of 709

The divisibility rule for 709 is a method by which we can find out if a number is divisible by 709 or not without using the division method. Let's check whether 2127 is divisible by 709 with the divisibility rule.

Step 1: Multiply the last digit of the number by 9, here in 2127, 7 is the last digit, multiply it by 9. 7 × 9 = 63

Step 2: Subtract the result from Step 1 from the remaining numbers but do not include the last digit. i.e., 212–63 = 149.

Step 3: As it is shown that 149 is not a multiple of 709, therefore, the number is not divisible by 709. If the result from step 2 is a multiple of 709, then the number is divisible by 709.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 709.

Know the multiples of 709:

Memorize the multiples of 709 (709, 1418, 2127, ... etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 709, then the number is divisible by 709.

Use the negative numbers:

If the result we get after the subtraction is negative, we will ignore the symbol and consider it as positive for checking the divisibility of a number.

 Repeat the process for large numbers:

Students should keep repeating the divisibility process until they reach a small number that is divisible by 709. For example: Check if 4253 is divisible by 709 using the divisibility test. Multiply the last digit by 9, i.e., 3 × 9 = 27. Subtract the remaining digits excluding the last digit by 27, 425–27 = 398. Still, 398 is a large number, hence we will repeat the process again and multiply the last digit by 9, 8 × 9 = 72. Now subtracting 72 from the remaining numbers excluding the last digit, 39–72 = -33. As -33 is not a multiple of 709, 4253 is not divisible by 709.

Use the division method to verify:

Students can use the division method as a way to verify and cross-check their results. This will help them to verify and also learn.

• Divisibility rule: A set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 2 if the number ends with an even digit.

• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 709 are 709, 1418, 2127, ...

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

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

• Verification: Verification is the process of confirming whether the result obtained is correct, often using an alternative method such as direct division.