Highest Common Factor

Highest common factor (H.C.F) of two or more numbers is the greatest number which divides each of them exactly.

Now we will learn about the method of finding highest common factor (H.C.F).

Steps 1:

Find all the factors of each given number.

Step 2:

Find common factors of the given number.

Step 3:

The greatest of all the factors obtained in Step 2, is the required highest common factor (H.C.F).

For Example:

1. Find the highest common factor (H.C.F) of 6 and 9.

Factors of 6 = 1, 2, 3 and 6.

Factors of 9 = 1, 3 and 9.

Therefore, common factor of 6 and 9 = 1 and 3.

Highest common factor (H.C.F) of 6 and 9 = 3.

Therefore, 3 is H.C.F. or G.C.D. greatest common divisor of 6 and 9.

H.C.F. or G.C.D. of given numbers is the greatest number which divides all the numbers without leaving a remainder.

2. Find the highest common factor (H.C.F) of 6 and 8.

Factors of 6 = 1, 2, 3 and 6.

Factors of 8 = 1, 2, 4 and 8.

Therefore, common factor of 6 and 8 = 1 and 2.

Highest common factor (H.C.F) of 6 and 8 = 2.

Therefore, 2 is H.C.F. or G.C.D. greatest common divisor of 6 and 8.

3. Find the highest common factor (H.C.F) of 14 and 18.

Factors of 14 = 1, 2, 7 and 14.

Factors of 18 = 1, 2, 3, 6, 9 and 18.

Therefore, common factor of 14 and 18 = 1 and 2.

Highest common factor (H.C.F) of 14 and 18 = 2.

Note: The highest common factor or HCF of two or more numbers is the greatest number that divides exactly the given numbers.

4. Find the highest common factor (H.C.F) of 15 and 10.

Factors of 15 = 1, 3, 5 and 15.

Factors of 10 = 1, 2, 5 and 10.

Therefore, common factor of 15 and 10 = 1 and 5.

Highest common factor (H.C.F) of 15 and 10 = 5.

5. Find the highest common factor (H.C.F) of 12 and 18.

Factors of 12 = 1, 2, 3, 4, 6 and 12.

Factors of 18 = 1, 2, 3, 6, 9 and 18.

Therefore, common factor of 12 and 18 = 1, 2, 3 and 6.

Highest common factor (H.C.F) of 12 and 18 = 6 [since 6 is the highest common factor].

6. Find the highest common factor (H.C.F) of 48 and 32.

Solution:

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48

Factors of 32 = 1, 2, 4, 8, 16 and 32

Therefore, the common factors are 1, 2, 4, 8 and 16.

The highest common factor is 16.

Thus, highest common factor (HCF) of 48 and 32 is 16.

The common factors can be represented using venn diagram as given below.

$Common Factors Using Venn Diagram$

7. Find the highest common factor (H.C.F) of 24 and 36.

Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24.

Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Therefore, common factor of 24 and 36 = 1, 2, 3, 4, 6, 8 and 12.

Highest common factor (H.C.F) of 24 and 36 = 12.

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