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Divisibility Test
Divisibility tests, often known as division rules in Math, are used to determine whether a number is divisible by another integer without using the division method. The quotient will be a whole number and the remainder will be zero if a number is totally divisible by another integer. If there is an integer q such that n=mq, a nonzero integer m divides an integer n. We use the notation m|n to express that m is a divisor of n and that m is a factor of n.
General Properties of Divisibility
Property 1 If a number is divisible by another number, it must be divisible by each other of the factors of that number.
Example We know that 36 is divisible by 12.
All factors of 12 are 1, 2, 3, 4, 6, 12
Property 2 If a number is divisible by each of two co-prime numbers, it must be divisible by their product.
Example We know that 4320 is divisible by each of the numbers 5 and 8. Also 5 and 8 co-primes. So 4320 must be divisible by 40. By long division, we find that it is true.
Property 3 If a number is a factor of each of the two given numbers, then it must be a factor of their sum.
Example We know that 7 is a factor of each of the numbers 49 and 63. So, 7 must be a factor of (49+63)=112. Clearly, 7 divides 112.
Property 4 If a number is a factor of each of the two given numbers then it must be a factor of their difference.
Example We know that 13 is a factor of each one of the numbers 65 and 117. So, 13 must be a factor of (117-65)=52. Clearly, 13 divides 52 exactly.
Test of Divisibility by 10
A number is divisible by 10 if it is one digit 0. Because the prime components of 10 are 5 and 2, numbers that are divisible by 10 must be even and divisible by 5. To put it another way, if a number is divisible by ten, the last digit must be a 0.
Example 20, 150, 650 and 500 are the numbers divisible by 10.
None of the numbers 3, 13, 56 and 7548 is divisible by 10.
Conclusion
We learnt about the properties of divisibility and how we go about determining which number is divisible by 10. Any number ending in zero is divisible by 10.
