What is 78 mod 7?

How to compute 78 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. 78 / 7 = 11.142857142857
2. ⌊11.142857142857⌋ = 11 (We only keep the integer part)
3. 7 × 11 = 77
4. 78 - 77 = 1 (Subtracting gives us the remainder)

In short: 78 − (7 × ⌊78 / 7⌋) = 1

Is 78 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 78 mod 7 is 1, this indicates that dividing 78 by 7 leaves a remainder of 1. Therefore, no, since the remainder isn't zero, 78 is not divisible by 7.