Mr. Peter has three pieces of wire of length 80 cm, 100 cm and 160 cm. He wishes to cut the three pieces of wire into smaller pieces of equal length with no remainder.
- What is the greatest possible length of each of the smaller pieces of wire?
- How many of the smaller pieces of wire of equal length can he get?
(a)
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Factors of 100:1, 2, 4, 5, 10, 20, 25, 50, 100
Factors of 160:1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
The highest common factor of 80, 100 and 160 is 20.
Greatest possible length of each smaller piece of wire = 20 cm
(b)
Total length of wire
= 100 + 160 + 80
= 340 cm
Number of smaller pieces
= 340 ÷ 20
= 17
Answer(s): 20 cm; (b) 17