Divisibility Rule of 71

The divisibility rule for 71 is a method by which we can find out if a number is divisible by 71 or not without using the division method. Check whether 4977 is divisible by 71 with the divisibility rule.

Step 1: Double the last digit of the number, here in 4977, 7 is the last digit, so double it. 7 × 2 = 14.

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 497–14 = 483.

Step 3: As it is shown that 483 is not a multiple of 71, continue the process: double the last digit of 483, which is 3, so 3 × 2 = 6. Subtract 6 from the remaining part, 48–6 = 42.

Step 4: Since 42 is not a multiple of 71, 4977 is not divisible by 71. If the result from the steps becomes a multiple of 71, then the number is divisible by 71.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 71.

• Know the multiples of 71: Memorize the multiples of 71 (71, 142, 213, 284…etc.) to quickly check the divisibility. The result from the subtraction should be a multiple of 71 for the number to be divisible by 71.

• Use 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 71.
  
  For example, check if 5681 is divisible by 71 using the divisibility test. Double the last digit, 1 × 2 = 2. Subtract the remaining digits excluding the last digit by 2, 568–2 = 566.
  
  Since 566 is a large number, continue the process: double the last digit of 566, 6 × 2 = 12. Subtract 12 from the remaining numbers excluding the last digit, 56–12 = 44.
  
  Since 44 is not a multiple of 71, 5681 is not divisible by 71.

• 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: A set of steps used to find out whether a number is divisible by another number without performing division.

• Multiples: Results obtained from multiplying a number by an integer. For example, multiples of 71 are 71, 142, 213, 284, etc.

• Integers: Whole numbers, which include negative numbers, positive numbers, and zero.

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

• Positive and Negative Numbers: Positive numbers are greater than zero, while negative numbers are less than zero. In divisibility tests, negative results are treated as positive.