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Divisibility Test
Divisibility tests, often known as division rules in Math, are used to see if a number is divisible by another integer without having to utilize the division method. If a number is completely divisible by another integer, the quotient will be a whole number and the remainder will be zero. A nonzero integer m divides an integer n if there is an integer q such that n=mq. To state that m is a divisor of n and that m is a factor of n, we use the notation m|n.
General 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 clear.
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.
Divisibility by 16
Rule 1: Consider the last three digits if the thousandth digit is even.
- Four times the remaining number plus the last two digits
- The original number must also be divisible by 16 if the outcome is divisible by 16.
Rule 2: If the thousandth digit is odd, follow this rule.
- Follow these steps:
- Take a look at the last three digits.
- Add 8 to the total.
- The original number must also be divisible by 16 if the outcome is divisible by 16.
If the thousands digit is even and the last three digits create a number that is divisible by 16, the number is divisible by 16. If the thousands digit is odd, and the number generated by the last three digits plus 8 is divisible by 16, the number is also divisible by 16.
Conclusion
Here we learnt about the divisibility test of 16. Any given number is divisible by 16 if the last four digits are divisible by 16. Also, when we add the last two digits to four times the rest, the number is divisible by 16.
