What is the highest common factor of 54 and 42?

The highest common factor (HCF) of 54 and 42 is 6.

The highest common factor, often abbreviated as HCF, also known as the greatest common divisor (GCD), is the largest positive integer that divides two or more given integers without leaving a remainder. It's a fundamental concept in number theory used to simplify fractions and solve various mathematical problems.

How to Find the Highest Common Factor

To determine the HCF of 54 and 42, we list all the factors (numbers that divide evenly) for each number and then identify the largest factor they share.

List the Factors of Each Number:
- Factors of 42: These are the numbers that divide 42 precisely.
  1, 2, 3, 6, 7, 14, 21, 42
- Factors of 54: These are the numbers that divide 54 precisely.
  1, 2, 3, 6, 9, 18, 27, 54
Identify Common Factors:
Next, we look for the factors that appear in both lists.
- Common factors of 42 and 54 are: 1, 2, 3, 6
Select the Highest Common Factor:
From the list of common factors, the largest number is the HCF. In this case, the highest common factor is 6.

Visualizing the Factors

A table can clearly show the factors for both numbers:

Number	Factors
42	1, 2, 3, 6, 7, 14, 21, 42
54	1, 2, 3, 6, 9, 18, 27, 54

As highlighted, 6 is the greatest number that appears in both factor lists.

Practical Application of HCF

Understanding the HCF can be useful in real-world scenarios. For example, imagine you have 42 red candies and 54 blue candies, and you want to create the largest possible number of identical bags, with each bag containing the same amount of red and blue candies, and no candies left over.

You would find the HCF of 42 and 54, which is 6.
This means you can make 6 identical bags.
Each bag would contain 7 red candies (42 ÷ 6 = 7) and 9 blue candies (54 ÷ 6 = 9).

This demonstrates how the HCF helps in dividing quantities into the largest possible equal groups. For further reading on this mathematical concept, you can explore resources on Greatest Common Factor (GCF).