Highest Common Factor

The Highest Common Factor is the largest factor common to two or more numbers.  Even at the basic mathematics level it may be abbreviated to H.C.F. in questions, so ensure your student is familiar with this presentation also.

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Your student must be confident with multiplication before attempting these types of questions.

Find the Highest Common Factor of a group of numbers.

To find the HCF of a group of numbers you follow these simple steps:

  1. Find all the factors of each number
  2. Identify the largest number common to ALL the numbers
  3. Write your answer as: HCF = (your chosen number)


Find the Highest Common Factor of 10 and 25

Step 1:

Find all the factors of each number

Factors of 10

1 , 2, 5 & 10

Factors of 25

1 , 5,  25

Step 2:

Identify the largest factor common to ALL the numbers

Factors of 10:  1 , 2, 5 & 10

Factors of 25: 1 , 5,  25

Although 10 and 25 are obviously larger factors than 5, they are not COMMON to both numbers.

Answer: HCF of 10 & 25 is 5

This is a skill that is essential to master for later mathematical success.  Be sure to get some of our Highest Common Factor Worksheets to get all the practice you need, or explore everything else Printable Math Worksheets has to offer.


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