Question

Find the length of the largest which piece of wood used to measure exactly the lengths 4 m, 50 cm and 6 m 30 cm woods.( Use repeated subtraction method)

Answer 1

Piece 1 of wood length = 4 m 50 cm ; 1m = 100 cm

∴ 4m 50 cm = 4 x 100 + 50 = 450 cm

Piece 2 of wood length = 6 m 30 cm = 6 x 100 + 30 = 630 cm

Now, we need to find the HCF of 450 & 630 by repeated subtraction method.

Let bigger number be m & smaller number be n

Therefore, m = 630 & n = 450

m – n = 630 – 450 = 180; now m = 450, n = 180

m – n = 450 – 180 = 270; now m = 180, n = 270

n – m = 270 – 180 = 90; now m = 180, n = 90

m – n = 180 – 90 = 90

∴ now m = n …90 is HCF

Answer:

Length of largest peice of wood to measure exactly the length of both pieces of wood is 90 cm