Question

A trader has three bundles of string 392 m, 308 m and 490 m long. What is the great est length of string that the bundles can be cut up into without any left over string?

Answer 1

The greatest length of string that the bundles can be cut up into without any left over the string is given by the HCF of 392, 308, and 490.

2	392
2	196
2	98
7	49
7	7
	1

 

2	308
2	154
7	77
11	11
	1

 

2	490
5	245
7	49
7	7
	1

392 = 2 × 2 × 2 × 7 × 7

308 = 2 × 2 × 7 × 11

490 = 2 × 5 × 7 × 7

∴ HCF = 2 × 7 = 14

Hence, the greatest length of string that the bundles can be cut up into without any left-over string is 14 m.