A divisor is the number you divide by. In 56 ÷ 8 = 7, the divisor is 8: it tells how many equal groups to make, or how big each group is. The divisor can never be 0. A divisor of a whole number is also one of its factors, because it divides that number with no remainder.
In Spanish
divisor
Also called
number you divide by, denominator (in a fraction), factor (of a whole number)
The divisor sets the number of equal parts. Split 24 into more parts and each part gets smaller.
Formal definition and notation
In a divisiona ÷ b, the numberb is the divisor, and b ≠ 0. For whole numbers, d is a divisor of n (written d ∣ n) when n = d × k for some whole number k; in this sense divisor and factor mean the same thing. For example, the divisors of 18 are 1, 2, 3, 6, 9 and 18.
Symbol
Read it as
Meaning
a ÷ b
a divided by b
b, after the sign, is the divisor
d ∣ n
d divides n
d is a divisor of n: 4 ∣ 20
Key facts
The divisor is after ÷, under the fraction bar, and outside the long-division bracket.
In a fraction, the divisor is the denominator: 34 = 3 ÷ 4.
The remainder is always less than the divisor: in 29 ÷ 6 = 4 R 5, 5 < 6.
Dividing by 1 leaves the dividend unchanged, and dividing by 0 is undefined.
For a positive dividend, a divisor between 0 and 1 makes the quotient larger than the dividend: 10 ÷ 0.5 = 20.
Every whole number n > 1 has at least two divisors, 1 and n; primes have exactly those two.
The denominator is the divisor written under a fraction bar. In 23, 3 is both the denominator and the divisor of 2 ÷ 3.
Quick check: 3 questions
Question 1 of 3
In 84 ÷ 7 = 12, which number is the divisor?
Show answer and explanation
Answer: C. You divide by 7, so 7 is the divisor. 84 is the dividend, 12 is the quotient and 91 adds 84 and 7.
Question 2 of 3
Which number is a divisor of 42?
Show answer and explanation
Answer: D.42 ÷ 14 = 3 exactly, so 14 is a divisor. 8, 12 and 5 leave remainders (2, 6 and 2).
Question 3 of 3
Find the divisor: 180 ÷ □ = 15.
Show answer and explanation
Answer: A.180 ÷ 15 = 12, and 180 ÷ 12 = 15. 165 subtracts, 195 adds, and 2700 multiplies.
Divisor: frequently asked questions
Is a divisor the same as a factor?
For whole numbers, yes. If 6 divides 24 with no remainder, then 6 is a divisor of 24 and also a factor of 24, because 6 × 4 = 24. The word divisor is also used for any number you divide by, even when there is a remainder: in 25 ÷ 6, 6 is the divisor but not a factor of 25.
Why can the divisor not be zero?
Division asks what number times the divisor gives the dividend. For 12 ÷ 0, you would need a number that gives 12 when multiplied by 0, but every number times 0 is 0. No such number exists, so 12 ÷ 0 is undefined. Even 0 ÷ 0 is undefined, because every number would work.
DivisionDivision is the operation of splitting a number into equal groups. In 12 ÷ 3 = 4, the dividend 12 is shared into 3 equal groups (the divisor), and each group gets 4 (the quotient). Division undoes multiplication, because 3 × 4 = 12. If the groups do not come out even, the amount left over is the remainder.Operations · Grade 3, Grade 4, Grade 5NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Whole NumberA whole number is 0 or a positive counting number: 0, 1, 2, 3, and so on. Whole numbers do not include fractions, decimals, or negative numbers, so 12 is a whole number but 8.5, 34 and −3 are not. Every whole number is also an integer.Number System · Grade 3, Grade 4, Grade 5DenominatorThe denominator is the bottom number in a fraction. It tells how many equal parts make one whole: in 35, the 5 means the whole is cut into 5 equal parts, and the numerator 3 counts the parts you have. The denominator can never be 0.Number System · Grade 3, Grade 4, Grade 5RemainderA remainder is the amount left over when one whole number does not divide another evenly. In 23 ÷ 5, four groups of 5 make 20 and 3 are left, so 23 ÷ 5 = 4 R 3. The remainder is always smaller than the divisor. A remainder of 0 means the division is exact.Operations · Grade 4, Grade 5, Grade 6DividendThe dividend is the number being divided in a division problem. In 56 ÷ 8 = 7, the dividend is 56, the divisor is 8 and the quotient is 7. It is the total you start with before splitting it into equal groups. In a fraction such as 568, the dividend is the numerator.Operations · Grade 3, Grade 4, Grade 5UndefinedUndefined describes an expression that has no value, most often because it divides by zero. 70 is undefined, since no number times 0 gives 7. A vertical line has an undefined slope, and 3x − 2 is undefined at x = 2. Undefined does not mean zero: 07 = 0, but 70 has no value.Problem Solving · Grade 6, Grade 8, Algebra 1QuotientA quotient is the answer you get when you divide one number by another. In 20 ÷ 4 = 5, the quotient is 5. The number being divided is the dividend and the number you divide by is the divisor. When the division is not exact, the quotient comes with a remainder, or as a decimal or fraction.Operations · Grade 3, Grade 4, Grade 5MultiplicationMultiplication is the operation that combines equal groups to find a total. The fact 4 × 6 = 24 means 4 groups of 6, or 6 + 6 + 6 + 6. The numbers you multiply are called factors, and the result is the product. Order does not matter: 6 × 4 is also 24.Operations · Grade 2, Grade 3, Grade 4Divisibility RulesDivisibility rules are shortcuts that tell whether one whole number divides another with no remainder, without doing the division. A number is divisible by 2 if its last digit is even, by 3 if its digit sum is divisible by 3, by 5 if it ends in 0 or 5, and by 10 if it ends in 0.Number System · Grade 4, Grade 5, Grade 6Long DivisionLong division is a step-by-step written method for dividing large numbers. You work through the dividend one digit at a time from the left, repeating four steps: divide, multiply, subtract, bring down. For 872 ÷ 4, the steps give the quotient 218 with a remainder of 0.Operations · Grade 4, Grade 5, Grade 6Greatest Common FactorThe greatest common factor (GCF) is the largest factor shared by two or more numbers: the largest number that divides into both without a remainder. The GCF of 18 and 24 is 6. Find it by listing factors or by multiplying the prime factors the numbers share. The GCF is how you simplify fractions in one step.Number System · Grade 5, Grade 6, Grade 7FactorA factor is a number or expression that divides another number or expression evenly, with no remainder. Factors multiply together to make a product: 4 × 6 = 24, so 4 and 6 are factors of 24. Every whole number greater than 1 has at least two factors, 1 and itself.Number System · Grade 4, Grade 5, Grade 6