Test of Divisibility

Test of Divisibility 

A divisibility test is a kind of shortcut that helps us to identify if a given integer is divisible by a divisor by examining its digits without performing the whole division process. Multiple divisibility rules can be applied to the same number, which can quickly determine its prime factorisation. A divisor of a number is an integer that completely divides the number without leaving any remainder. Martin Gardner, a prominent math and science writer, discussed divisibility principles for 2–12 in a 1962 Scientific American article, explaining that the rules were well-known during the Renaissance and were used to reduce fractions with high numbers to their simplest terms. Because no number is totally divided by any other integer, a leftover other than zero may be left. There are some rules that can help us figure out what a number’s true divisor is merely by looking at its digits. There are numerous tests of divisibility worksheets available on the internet for further practice sums on the same.

Properties Of Divisibility

Property 1: If a number is divisible by another number, it must also be divisible by each of its factors.

Example We already know that 36 may be divided by 12.

All 12 components are 1, 2, 3, 4, 6, and 12.

Property 2: If a number is divisible by each of two co-prime integers, it must also be divisible by the product of those numbers.

Example We know that 972 is divisible by each one of the numbers 2 and 3. Also, 2 and 3 are co-primes.

Property 3: If a number is a factor of both the supplied numbers, it must also be a factor of their sum.

Example We know that 5 is a factor of 15 as well as that of 20. So, 5 must be a factor of (15+20), that is 35. And, this is clearly dividing 35.

Property 4: If a number is a factor of both the given numbers, it must also be a factor of the difference between them.

Example We know that 3 is a factor of each one of the numbers 36 and 24. So, 3 must be a factor of (36-24) = 12. Clearly, 3 divides 12 exactly.

Test of Divisibility of Numbers

Here is the Divisibility Test of Numbers of numbers from 2 to 12. 

• Divisibility by 2: Any number ending in an even number that is 0, 2, 4, 6, and 8 is divisible by 2.

• Divisibility by 3: The sum of all the digits in a number should be divisible by 3.

• Divisibility by 4: The last two digits of the number should be either divisible by 4 or be 00.

• Divisibility by 5: The numbers ending in either 0 or 5 are divisible by 5.

• Divisibility by 6: The number should be divisible by both 2 and 3, then the number divisible by 6.

• • Divisibility by 7: A multiple of 7 is obtained by subtracting twice the number’s last digit from the remaining digits.

• Divisibility by 8: The last three digits of the number should either be divisible by 8 or be 000.

• Divisibility by 9: The sum of all the digits in the number should be divisible by 9.

• Divisibility by 10: The number which has digit zero at its one’s place is divisible by 10.

• Divisibility by 11: The difference between the sums of a number’s alternate digits is divisible by 11.
• Divisibility by 12: The number should be divisible by both 3 and 4, then the number is divisible by 12.

Conclusion

A divisibility test is a quick approach to see if a given number can be divided by a predetermined divisor without having to do the division yourself. When a number is divided fully by another number, the quotient must be a whole number, and the remainder must be zero. We looked upon the divisibility test from 2 and 12 and how we go about checking it for different numbers.