Word Problems on H.C.F.
Let us consider some of the word problems on H.C.F. (highest common factor).
1. Two wires are 12 m and 16 m long. The wires are to be cut into pieces of equal length. Find the maximum length of each piece.
To find the maximum length, we find the H.C.F. of 12 and 16
Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 16: 1, 2, 4, 8, 16

1 × 12, 2 × 6, 3 × 4 1 × 16, 2 × 8, 4 × 4

H.C.F. = 4
The maximum length of each piece is 4 m.
2. Find the greatest number which is less by 2 to divide 24, 28 and 64 exactly.
First we find the H.C.F. of 24, 28 and 64.
H.C.F. = 4
The required number is 4  2 = 2.
(We see that 2 is less than 4 by 2.)
3. Find the greatest number that divides 90 and 126 exactly.
Solution:
The greatest number that divides both 90 and 126 exactly is
their HCF.
We can find HCF by long division method.
HCF of 90 and 126 is 18.
4. Rachel has 24 red candies and Maya has 18 green candies. They want to arrange the candies in such a way that each row contains equal number of candies and also each row should have only red candies or green candies. What is the greatest number of candies that can be arranged in each row?
Solution:
In order to find the greatest number of candies that can be arranged in equal rows, we find the HCF of two numbers.
Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Factors of 18 are 1, 2, 3, 6, 9 and 18.
The highest common factor is 6.
So, the greatest number of candies that can be arranged in each row is 6.
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