Divisibility Rule of 59

The divisibility rule for 59 is a method by which we can find out if a number is divisible by 59 or not without using the division method. Check whether 1180 is divisible by 59 with the divisibility rule.

Step 1: Multiply the last digit of the number by 5, here in 1180, 0 is the last digit. Multiply it by 5. 0 × 5 = 0

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 118–0 = 118.

Step 3: As it is shown that 118 is not a multiple of 59, repeat the process: 

Repeat Step 1 with the new number: Multiply the last digit of 118 by 5. 8 × 5 = 40

Subtract from the remaining digits: 11–40 = -29.

Step 4: Consider the absolute value for divisibility check. As 29 (absolute value of -29) is not a multiple of 59, the number 1180 is not divisible by 59. 

If the result from the subtraction is a multiple of 59, then the original number is divisible by 59.

Learning the divisibility rule can help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 59.

Know the multiples of 59:

Memorize the multiples of 59 (59, 118, 177, 236, 295… etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 59, then the number is divisible by 59.

Use the negative numbers:

If the result we get after the subtraction is negative, we will avoid 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 59. 

For example: Check if 3541 is divisible by 59 using the divisibility test. Multiply the last digit by 5, i.e., 1 × 5 = 5. Subtract from the remaining digits, 354–5 = 349.

Since 349 is a large number, repeat the process:

Multiply the last digit by 5, 9 × 5 = 45.

Subtract from the remaining digits, 34–45 = -11.

Since 11 is not a multiple of 59, 3541 is not divisible by 59.

Use the division method to verify:

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

• Divisibility rule: The 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 even numbers.

• Multiples: Multiples are the results we get after multiplying a number by an integer. For example: multiples of 59 are 59, 118, 177, 236, 295, etc.

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

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

• Absolute value: The absolute value of a number is its distance from zero on the number line, without considering its sign. For example, the absolute value of -11 is 11.