Divisor — Definition, Formula & Examples

Divisor

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See also

Key Formula

a \div b = c

Where:

$a$ = The dividend (the number being divided)
$b$ = The divisor (the number you divide by)
$c$ = The quotient (the result)

Worked Example

Problem: Identify the divisor in 56 ÷ 8 = 7, and verify the division.

Step 1: Identify each part of the division statement.

56 \div 8 = 7

Step 2: The dividend is 56 (the number being divided). The divisor is 8 (the number you divide by). The quotient is 7 (the result).

Step 3: Verify by multiplying the divisor by the quotient to recover the dividend.

8 \times 7 = 56 \checkmark

Answer: The divisor is 8.

Why It Matters

Understanding the role of the divisor is essential whenever you work with fractions, since the denominator of a fraction acts as the divisor. Recognizing divisors also helps you find factors of a number, determine divisibility, and simplify expressions throughout algebra and number theory.

Common Mistakes

Mistake: Confusing the divisor with the dividend.

Correction: Remember that the divisor is the number you divide by, not the number being divided. In

a \div b

b

is the divisor and

a

is the dividend.

Related Terms

Dividend — The number being divided by the divisor
Quotient — The result of dividing by a divisor
Factor — A divisor that divides a number evenly
Divisible — Describes a number with no remainder after division
Remainder — The amount left over after division