EDEXCEL GCSE FOUNDATION MATHS - What are Multiples and Factors

Edexcel GCSE Foundation Maths: Multiples and Factors

What are Multiples?

• A multiple of a number is the result of multiplying that number by a whole number.
• For example, the multiples of 3 are: 3, 6, 9, 12, 15, 18, and so on.
• You can find multiples of a number by repeatedly adding that number to itself.

What are Factors?

• A factor of a number is a number that divides evenly into it.
• For example, the factors of 12 are: 1, 2, 3, 4, 6, and 12.
• You can find factors of a number by finding all the numbers that divide into it without leaving a remainder.

Finding Multiples and Factors:

Multiples:

• To find the first few multiples of a number, simply multiply that number by 1, 2, 3, 4, and so on.
• To find all the multiples of a number, you can use a number line or a multiplication table.

Factors:

• To find the factors of a number, start by dividing the number by 1, then by 2, and so on, until you reach the number itself.
• If the division results in a whole number, then that number is a factor.
• Example: Finding the factors of 24
  • 24 ÷ 1 = 24 (1 is a factor)
  • 24 ÷ 2 = 12 (2 is a factor)
  • 24 ÷ 3 = 8 (3 is a factor)
  • 24 ÷ 4 = 6 (4 is a factor)
  • 24 ÷ 6 = 4 (6 is a factor)
  • 24 ÷ 8 = 3 (8 is a factor)
  • 24 ÷ 12 = 2 (12 is a factor)
  • 24 ÷ 24 = 1 (24 is a factor)
• Therefore, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Key Points:

• Every number has at least two factors: 1 and itself.
• Prime numbers have only two factors: 1 and itself.
• 1 is not a prime number.

Practice:

1. Find the first five multiples of 7.
2. Find all the factors of 36.
3. What are the common factors of 12 and 18?
4. What are the first three common multiples of 4 and 6?

By understanding multiples and factors, you can solve many different types of problems in Edexcel GCSE Foundation Maths.