Divisor facts for kids

When you divide one number by another, and there's nothing left over, the number you divided by is called a divisor. It's also known as a factor.

For example, if you divide 10 by 2, you get 5 with no remainder. So, 2 is a divisor of 10. Every number can always be divided evenly by 1 and by itself. These are always divisors. A prime number is a special kind of number that only has two divisors: 1 and itself. Finding the divisors of a number is called factorization.

What is a Divisor?

Let's look at an example. The number 7 is a divisor of 42 because 42 divided by 7 equals 6. There is no remainder. When this happens, we can say a few things:

• "42 is divisible by 7"
• "42 is a multiple of 7"
• "7 divides 42"
• "7 is a factor of 42"

The positive divisors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. Sometimes, people also include negative numbers as divisors. For example, -2 is a divisor of 4 because 4 divided by -2 equals -2. However, usually, when we talk about divisors, we mean the positive ones.

Special Divisors

• The numbers 1 and -1 are divisors of every integer.
• Every integer is a divisor of itself.
• Every integer (except 0) is a divisor of 0.
• Numbers that can be divided by 2 are called even.
• Numbers that cannot be divided by 2 are called odd.

A divisor of a number n that is not 1, -1, n, or -n is called a non-trivial divisor.

• If a number has non-trivial divisors, it's called a composite number.
• If a number has no non-trivial divisors (only 1 and itself as positive divisors), it's a prime number.

The word "divisor" comes from the math operation of division. In a division problem like a ÷ b = c:

• a is the dividend (the number being divided).
• b is the divisor (the number doing the dividing).
• c is the quotient (the answer).

How to Spot Divisors

There are some cool "math tricks" or rules that help you quickly find certain divisors of a number just by looking at its digits.

For example:

• If the last digit of a number is even (0, 2, 4, 6, or 8), then 2 is a divisor.
• If the last digit is 0 or 5, then 5 is a divisor.
• If you add up all the digits of a number, and the sum is a multiple of 3, then 3 is a divisor.

Let's look at the number 340:

• It ends in "0", so 2 and 5 are both divisors.
• Since both 2 and 5 are divisors, their product (2 × 5 = 10) is also a divisor.
• If we divide 340 by 10, we get 34.
• We can break down 34 into 2 × 17.
• So, the positive divisors of 340 are: 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, and 340.

Remember, 1 and the number itself are always divisors!

Related pages

• Coprime
• Euclid's lemma

Images for kids

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  The divisors of 10 illustrated with Cuisenaire rods: 1, 2, 5, and 10

See also

In Spanish: Divisibilidad para niños