What is 77 mod 7?

How to compute 77 mod 7?

The simplest approach is to use the "mod" operator (often denoted as "%" in many programming languages), but you could do it manually in the following way:

$\mathrm{Remainder}=N-(M\times \lfloor \frac{N}{M}\rfloor )$

(where N is the dividend, M is the divisor and $\lfloor \frac{N}{M}\rfloor$ represents the integer part of the quotient)

1. 77 / 7 = 11
2. ⌊11⌋ = 11 (We only keep the integer part)
3. 7 × 11 = 77
4. 77 - 77 = 0 (Subtracting gives us the remainder)

In short: 77 − (7 × ⌊77 / 7⌋) = 0

Is 77 divisible by 7?

A number is said to be divisible by another number, if the remainder of the division is zero.

Given that the result of 77 mod 7 is 0, this indicates that dividing 77 by 7 leaves no remainder. Therefore, yes, 77 is indeed divisible by 7.