Page 68 - ICSE Math 5

4. Check the divisibility of the following numbers by 2, 3, 4, 5, 6, 8, 9, 10 and 11. Tick ( )

the box, if the numbers are divisible and cross (), if they are not.

Number 2 3 4 5 6 8 9 10 11

5,381

81,620

61,800

65,175

4,26,972

Highest Common Factor (H.C.F.)

The Highest Common Factor or H.C.F. of two or more numbers is their greatest common factor.
H.C.F. is also known as the Greatest Common Factor (G.C.F.) or the Greatest Common Divisor
(G.C.D).

We can find the H.C.F. of the given numbers either by listing method or by common division
method.
Example 15: Find the H.C.F. of 28 and 72 using listing method.

Solution: Step 1: List the factors of 28 and 72 separately.
Factors of 28 = 1 , 2 , 4 , 7, 14 and 28

Factors of 72 = 1 , 2 , 3, 4 , 6, 8, 9, 12, 18, 24, 36 and 72
Step 2: Compare and identify the common factors of 28 and 72.

Common factors of 28 and 72 = 1, 2, and 4
Step 3: Write the H.C.F. of 28 and 72.

So, the H.C.F. of 28 and 72 is 4.
Example 16: Find the H.C.F. of 24, 48 and 64 using common division method.

Solution: Step 1: Write 24, 48 and 64 in a row separated by commas.
2 24, 48, 64
Step 2: Divide them by their smallest common factor and
2 12, 24, 32
write down the quotients in next row.
2 6, 12, 16
Step 3: Divide numbers in next row by their smallest common 3, 6, 8
factor and write down the new quotients in next row.
Step 4: Repeat this process until the quotients obtained have no common
factor.

Step 5: Multiply the common factors that are on the left column to obtain the
H.C.F.
So, the H.C.F. of 24, 48 and 64 = 2 × 2 × 2 = 8.

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