Answer:
a) 16 cm, b) 37 pieces
Step-by-step explanation:
Part a
Finding the largest divisor of 160, 192 and 240
160 divisors: 1, 2, 4, 5, 8, 10, 16, 32, 40, 80 and 160.
// You can alternatively find them by factor pairs, which are (1, 160), (2, 80), (4, 40), (5, 32), (8, 20) & (10, 16). This way is much more faster. Also, you can simply search them in metanumbers.com
192 divisors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 and 192
240 divisors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240
The largest divider that they all have in common is 16.
So 16 cm is the largest possible length of each of the shorter pieces of
rope
Part b
Now we have to count how many 16 cm pieces of rope can we get from the large rope pieces, which lengths are 160 cm, 192 cm and 240 cm
160/16 + 192/16 + 240/16 = 10 + 12 + 15 = 37
The answer is 37 pieces
