Can an integer be divisible by 2?

An integer is divisible by 2 if its last digit is 0,2,4,6 or 8 . (In other words, if it’s even.) 754 is divisible by 2 , since its last digit is 4 . 8267 is not divisible by 2 , since its last digit is not one of 0,2,4,6 or 8 .

When can a number be divisible by 2?

All even numbers are divisible by 2. Therefore, a number is divisible by 2 if it has a 0, 2, 4, 6, or 8 in the ones place. For example, 54 and 2,870 are divisible by 2, but 2,221 is not divisible by 2. A number is divisible by 4 if its last two digits are divisible by 4.

How do you prove divisible by 2?

A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8. Numbers divisible by 2 are called even numbers.

What is the value of n if n is not divisible by 3?

If n not divisible by 3, then either n=3k+1 or n=3l+2 now lets square it in first case n 2 = (9 k 2 + 6 k + 1) = 3 (3 k 2 + 2 k) + 1 = 3m +1 in second case = 9 k 2 + 12k + 4 = 3 (3 k 2 + 4 k + 1) + 1 = 3m + 1

How do you prove that a number is divisible by 6?

Out of three (n – 1), n, (n + 1) one must be even, so a is divisible by 2. 2. (n – 1) , n, (n + 1) are consecutive integers thus as proved a must be divisible by 3. Thus, n³ – n is divisible by 6 for any positive integer n. When a number is divided by 3, the possible remainders are 0 or 1 or 2. ∴ n = 3p or 3p + 1 or 3p + 2, where r is some integer.

How do you prove 3 does not divide n?

Suppose that 3 does not divide n, then G C D ( 3, n) = 1 and there are integers a and b such that 3 a + n b = 1. Now if you multiply both sides by n you get 3 a n + n 2 b = n. 3 divides the left hand side, so it divides n too, which gives the desired contradiction.

Which equation is divisible by 3?

The statement is vacuously true for n = 1, 2 and obviously true for n = 3. Here P = n*3 ==> divisible by 3 Q = (n-1) n (n+1) ==> this is multiplication of three consecutive number and hence it is divisible by 3 ==> P + Q is divisible by 3