What is a common factor in maths? - BBC Bitesize (2024)

• A is a whole number which is a of two or more numbers.

• The (HCF) is the greatest factor that will divide into two or more numbers.

• The (LCM) is the smallest that is common to two or more numbers.

• The HCF and LCM:

  • are used when adding and subtracting fractions.
  • can be found by listing factors and multiples. For larger values, expressing numbers as a is a more efficient method. A can also be used.

Knowing how to find factors, draw and write numbers as a product of their prime factors is useful to know when finding common factors, the HCF and LCM.

• A is a whole number which is a of two or more numbers. Eg, 2, 5 and 10 are common factors of 30 and 20

• 1 is a common factor of all whole numbers.

To find common factors:

1. List the factors of each number.

2. Compare the factors to find numbers that are the same (or common) in each list.

The (HCF) is the greatest factor that will divide into two or more numbers.

The HCF of two or more numbers can be found by listing the factors. For larger numbers, can be used. Prime factorisation means expressing the numbers as a .

By listing:

1. List the factors of each number.

2. Compare the lists to find the greatest number common to both.

By prime factorisation:

1. Draw for each number. You may need to review how to draw a factor tree.

2. Write each number as a product of its prime factors. It can be easier to not use form.

3. Identify the common in each product of prime factors.

4. To find the HCF, multiply the common prime factors.

Remember: index form is an abbreviation for repeated multiplication. Eg, 5² means 5 × 5. 5³ means 5 × 5 × 5

• A is an that is in the multiplication table of a specific number.

• The (LCM) is the lowest multiple that is common to two or more numbers.

The lowest common multiple (LCM) of two of more numbers can be found by listing the numbers. For larger numbers, can be used.

By listing

1. List consecutive multiples for each number.

2. The first multiple to occur in every list is the LCM.

By prime factorisation

1. Draw for each number.

2. Write each number as a . It can be easier to not use form.

3. Identify the common prime factors in each product of .

4. The prime factors that are not common to each product are unique for that number.

   See Also

   HCF - Highest Common Factor - Definition, How to Find HCF? | HCF Examples

5. To find the LCM, multiply the common factors by the unique factors of one number and the unique factors of the other number.

To use a to find the HCF and LCM of two numbers:

1. Write each number as a without using index form.

2. Draw a Venn diagram:

• Draw a circle for each number.

• Place the factors that are common to both numbers in the intersection (the overlap) of the circles.

• Place the remaining prime factors for the first number in its circle.

• Place the remaining for the second number in its circle.

• Check that each circle contains the full for each number.

3. To find the HCF of the numbers - multiply the numbers in the intersection.

4. To find the LCM of the numbers - multiply all the numbers in the circles in the Venn diagram.

The HCF and LCM can be useful for a variety of businesses when ordering materials and stock.

Calculating the HCF can help an independent stationery business to use their materials efficiently – for example, when making cards. Card stock can be bought in lengths of 24 inches and 36 inches. The HCF of 24 and 36 is 12. By making cards at a size of 12 inches, they can limit the amount of waste produced from card stock.

Calculating the LCM can allow an event planner to manage their budget effectively. For example, they may want to order the same amount of stickers and tote bags to include in gift bags. If the stickers are sold in packs of 15 and gift bags are sold in packs of 6, they should buy these items in batches of 30. The LCM of 15 and 6 is 30. This means that 2 packs of stickers and 5 packs of tote bags gives 30 of each gift. This way, the event planner has matching amounts to put in the gift bags.