Highest common factor

Key Notes:

Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is the largest number that can exactly divide two or more numbers without leaving a remainder.

• Definition: A number that divides two or more numbers exactly.
• Example: For 12 and 18, common factors are 1, 2, 3, 6.

• Definition: The largest number that is a common factor of the given numbers.
• Example: For 12 and 18, the HCF is 6.

There are different methods to find the HCF:

List All Factors:

Identify Common Factors:

• Find the numbers that appear in both lists.
• Common Factors: 1, 2, 3, 6

Select the Greatest One:

• The HCF is the largest number in the list of common factors.
• HCF: 6

Prime Factorise Each Number:

Break each number into prime factors.

Example:

• 12 = 2² × 3

• 18 = 2 × 3²

Find the common prime factors.

Common Prime Factors: 2 and 3

Multiply the Lowest Powers:

• Multiply the common prime factors, using the smallest power for each prime.
• HCF: 2¹ × 3¹ = 6

Divide the Larger Number by the Smaller Number and Find the Remainder:

• Example: For 48 and 18:
• 48 ÷ 18 = 2 remainder 12

Replace the Larger Number with the Smaller Number and the Smaller Number with the Remainder:

• New numbers: 18 and 12.

Repeat Until the Remainder is 0:

• Continue the process until the remainder is 0.
• The divisor at this step is the HCF.

Simplifying Fractions:

• Helps in reducing fractions to their simplest form.

Solving Problems:

• Useful in problems related to grouping or arranging items.

Dividing Objects:

• Helps in dividing objects into equal parts without leftovers.

 12: 1, 2, 3, 4, 6, 12
 18: 1, 2, 3, 6, 9, 18

let’s practice!