Introduction to Factors and Multiples

Hello, Year 6! Today, we are going to learn about factors and multiples. These are important concepts in maths that help us work with numbers in different ways.

What are Factors?

Factors are the numbers you can multiply together to get another number. For example, if we take the number 12, the factors of 12 are the numbers that can be multiplied to equal 12.

Let’s find the factors of 12:

  • 1 × 12 = 12
  • 2 × 6 = 12
  • 3 × 4 = 12

So, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Key Rule for Factors:

  • A number is always a factor of itself.
  • 1 is a factor of every number.

What are Multiples?

Multiples are the numbers you get when you multiply a number by whole numbers. So, for the number 3, its multiples are:

  • 3 × 1 = 3
  • 3 × 2 = 6
  • 3 × 3 = 9
  • 3 × 4 = 12
  • 3 × 5 = 15

So, the first few multiples of 3 are 3, 6, 9, 12, and 15.

Key Rule for Multiples:

  • Zero is a multiple of every number.
  • The number itself is always a multiple (e.g., 3 is a multiple of 3).

Tips and Tricks

  1. Finding Factors:
    • Start with 1 and the number itself.
    • Check each number in between to see if it divides evenly (no remainder).
  2. Finding Multiples:
    • Just keep adding the number to itself. (For example: 3, 6, 9, 12…)
  3. Using a Factor Tree:
    • A factor tree can help you break down numbers into their prime factors. This is useful for bigger numbers!
  4. Remember:
    • Factors are found by division, while multiples are found by multiplication.

Questions

Easy Level Questions

  1. What are the factors of 10?
  2. List the first 5 multiples of 4.
  3. Is 6 a factor of 24?
  4. What are the factors of 8?
  5. Is 5 a multiple of 2?
  6. What is the smallest factor of any number?
  7. List the multiples of 1.
  8. What are the factors of 15?
  9. How many factors does the number 14 have?
  10. What is the 3rd multiple of 5?

Medium Level Questions

  1. What are the factors of 30?
  2. List the first 8 multiples of 7.
  3. What is the greatest factor of 18?
  4. Is 12 a factor of 36?
  5. What are the first 4 multiples of 9?
  6. Find the factors of 36.
  7. How many multiples of 6 are less than 50?
  8. Are all even numbers multiples of 2?
  9. What is the least common multiple (LCM) of 2 and 3?
  10. What are the factors of 24?

Hard Level Questions

  1. What is the prime factorisation of 60?
  2. List the first 10 multiples of 12.
  3. How many factors does the number 100 have?
  4. What is the greatest common factor (GCF) of 20 and 30?
  5. If a number has factors of 1, 2, 4, 8, what number is it?
  6. What is the least common multiple (LCM) of 4 and 5?
  7. Find the factors of 48.
  8. List the multiples of 11 up to 100.
  9. How many factors does the number 36 have?
  10. If 42 is a multiple of a number, what are the possible factors of that number?

Answers

Easy Level Answers

  1. 1, 2, 5, 10
  2. 4, 8, 12, 16, 20
  3. Yes
  4. 1, 2, 4, 8
  5. No
  6. 1
  7. 1
  8. 1, 3, 5, 15
  9. 4
  10. 15

Medium Level Answers

  1. 1, 2, 3, 5, 6, 10, 15, 30
  2. 7, 14, 21, 28, 35, 42, 49, 56
  3. 18
  4. Yes
  5. 9, 18, 27, 36
  6. 1, 2, 3, 4, 6, 9, 12, 18, 24, 36
  7. 8
  8. Yes
  9. 6
  10. 1, 2, 3, 4, 6, 8, 12, 24

Hard Level Answers

  1. 2 × 2 × 3 × 5
  2. 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
  3. 9
  4. 10
  5. 8
  6. 20
  7. 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
  8. 11, 22, 33, 44, 55, 66, 77, 88, 99
  9. 9
  10. 1, 2, 3, 6, 7, 14, 21, 42

Now you have a solid understanding of factors and multiples! Keep practicing, and you’ll get even better!