What is 100 mod 21?

How to compute 100 mod 21?

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. 100 / 21 = 4.7619047619048
2. ⌊4.7619047619048⌋ = 4 (We only keep the integer part)
3. 21 × 4 = 84
4. 100 - 84 = 16 (Subtracting gives us the remainder)

In short: 100 − (21 × ⌊100 / 21⌋) = 16

Is 100 divisible by 21?

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

Given that the result of 100 mod 21 is 16, this indicates that dividing 100 by 21 leaves a remainder of 16. Therefore, no, since the remainder isn't zero, 100 is not divisible by 21.