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.)
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