How do you find the factors of a number?

To find the factors, divide the number by integers starting from 1 up to the number itself. Any integer that divides the number exactly is a factor. Alternatively, you can use the prime factorization method.

What are prime factors?

Prime factors are factors that are prime numbers. For example, the prime factors of 18 are 2 and 3, since 18 = 2 × 3 × 3.

What is the smallest factor of any number?

The smallest factor of any non-zero number is 1.

What is the largest factor of a number?

The largest factor of a number is the number itself.

Can negative numbers have factors?

Yes, negative numbers have factors as well. For example, the factors of −6 are −1, −2, −3, −6, 1, 2, 3, 6.

What is a factor pair?

A factor pair is a set of two numbers that, when multiplied together, result in a given product. Example: For 12, factor pairs are (1, 12), (2, 6), (3, 4).

Can a prime number have factors?

Yes, but only two: 1 and the number itself. For example, the only factors of 7 are 1 and 7.

What are the factors of 0?

Technically, every non-zero integer is a factor of 0 because any number multiplied by 0 equals 0. However, in practical terms, factors of 0 are not usually discussed.

What is the difference between factors and divisors?

Factors and divisors are terms that are often used interchangeably. Both refer to numbers that divide another number evenly.

What are consecutive factors?

Consecutive factors are factors that follow each other without any gaps. For example, 1, 2, 3 are consecutive factors of 6.

How do factors relate to multiples?

If a number a is a factor of b, then b is a multiple of a. Example: If 4 is a factor of 12, then 12 is a multiple of 4.

Can the number of factors of a number be odd?

Yes, numbers that are perfect squares have an odd number of factors. Example: 36 has factors 1, 2, 3, 4, 6, 9, 12, 18, 36 (9 factors).

Factors - Online Coding and Math Classes for Kids

What Are Factors?

Factors are numbers that can multiply together to make another number. Think of them as the “building blocks” of a number! If you multiply two numbers and get a product, those numbers are called the factors of that product.

For example:

Factors of 12: 1, 2, 3, 4, 6, and 12, because:

How to Find Factors?

To find the factors of a number, just think of all the different ways you can multiply two numbers to get that number. Here’s how:

Start with 1: 1 is a factor of every number.
Go in order: Start with 1 and work your way up, checking if each number divides evenly.
Divide to check: If a number divides evenly (no remainder), it’s a factor!

Example: Finding the factors of 18

Start with 1: → So, 1 and 18 are factors.
Next, check 2: → So, 2 and 9 are factors.
Next, check 3: → So, 3 and 6 are factors.

So, the factors of 18 are: 1, 2, 3, 6, 9, and 18.

Points to Note

Every number has 1 and itself as factors. Example: For 7, the factors are 1 and 7.
Factors come in pairs. Example: For 12, the pairs are (1, 12), (2, 6), and (3, 4).
Prime numbers have only two factors: 1 and the number itself. Example: The only factors of 5 are 1 and 5.

Practice Time!

Find the factors of these numbers:

Common Factors

Common factors are factors that two or more numbers share. They are numbers that can divide each of the given numbers without leaving a remainder.

How to Find Common Factors?

List the Factors: Start by listing the factors of each number.
Identify the Common Ones: Look for the numbers that appear in both lists.

Example

Let’s find the common factors of 12 and 18.

Factors of 12:
- 1, 2, 3, 4, 6, 12
Factors of 18:
- 1, 2, 3, 6, 9, 18
Common Factors:
- The common factors are 1, 2, 3, and 6.

Understanding common factors is a key part of learning math. It helps us see the relationships between numbers and is especially helpful in working with fractions. We use it for simplifying fractions and for finding the highest common factor (HCF) or greatest common divisor (GCD).

Practice Quiz on Factors

FAQs on Factors

To find the factors, divide the number by integers starting from 1 up to the number itself. Any integer that divides the number exactly is a factor.
Alternatively, you can use the prime factorization method.

Prime factors are factors that are prime numbers. For example, the prime factors of 18 are 2 and 3, since 18=2×3×3.

The smallest factor of any non-zero number is 1.

The largest factor of a number is the number itself.

Yes, negative numbers have factors as well. For example, the factors of −6 are −1,−2,−3,−6,1,2,3,6.

A factor pair is a set of two numbers that, when multiplied together, result in a given product.
Example: For 12, factor pairs are (1,12),(2,6),(3,4).

Yes, but only two: 1 and the number itself. For example, the only factors of 7 are 1 and 7.

Technically, every non-zero integer is a factor of 0 because any number multiplied by 0 equals 0. However, in practical terms, factors of 0 are not usually discussed.

Factors and divisors are terms that are often used interchangeably. Both refer to numbers that divide another number evenly.

Consecutive factors are factors that follow each other without any gaps. For example, 1,2,3 are consecutive factors of 6.

If a number a is a factor of b, then b is a multiple of a.
Example: If 4 is a factor of 12, then 12 is a multiple of 4.

Yes, numbers that are perfect squares have an odd number of factors.
Example: 36 has factors 1,2,3,4,6,9,12,18,36 (9 factors).