This is the basic and conceptual question from real numbers in which we have to find the greatest possible length of each plank and also asked to find the number of planks formed by the three different lengths of plank 42m, 49m and 63m.

Kindly solve the above problem in detail

RS Aggarwal, Class 10, chapter 1B, question no 20

## Given : the lengths of three pieces of timber areÂ 42Â m,49Â m andÂ 63Â m respectively. we have to divide the timber into equal length of planks.

greatest possible length of each plankÂ =HCF(42,49,63)

The prime factorization ofÂ 42,49Â andÂ 63Â are:

42=2Ã—3Ã—7

49=7Ã—7

63=3Ã—3Ã—7

HCFÂ (42,49,63)=7

the greatest possible length of each plank isÂ 7Â m.

again, the number of planks can be formedÂ =22.