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# Remainder Calculator

## Remainder calculator helps you calculate the remainder and quotient.

What is the remainder

Remainder and quotient can be expressed with the following equality:

a = b × q + r

a - dividend
b - divisor (cannot be zero b ≠ 0)
q - quotient
r - remainder (0 ⩽ r ⩽ |b|)

If the dividend is less than the divisor, then the quotient is zero and the remainder is equal to the dividend. For example, 6: 12 = 0 (remainder = 6), 2: 9 = 0 (remainder = 2), 75 : 123 = 0 (remainder = 75).

Here are some examples

1) divide 17 by 7, then dividend a = 17, divisor b = 7. Substitute a and b into a = b × q + r.
17 = 7 × q + r
Now let's think about what we need to multiply 7 to get the number 17, there is no such number, but if 7 is multiplied by 2, then we get 14. You can also divide 17 by 7 on the calculator and the whole part to the decimal point will be q. Let's write the number 2 instead of q and find r.
17 = 7 × 2 + r
r = 17 - (7 × 2)
r = 3
Therefore, the remainder is 3, the quotient is 2.

2) divide 45 by 6, then dividend a = 45, divisor b = 6. Substitute the values ​​of a and b into a = b × q + r.
45 = 6 × q + r
Now let's think about what we need to multiply 6 to get the number 45, there is no such number, but if 6 is multiplied by 7, we get 42. Instead of q, write the number 7 and find r.
45 = 6 × 7 + r
r = 45 - (6 × 7)
r = 3
Therefore, the remainder is 3, the quotient is 7.

3) divide 72 by 12, then dividend a = 72, divisor b = 12. Substitute a and b into a = b × q + r.
72 = 12 × q + r
Now let's think about what you need to multiply 12 to get the number 72, the first thing to do is always try to divide the dividend by the divisor. 72: 12 = 6. The number 72 was divided by an integer by 12, hence the remainder of the division of these numbers is 0.
72 = 12 × 6 + 0
r = 0

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