Mr. Ethan has three pieces of wire of length 40 cm, 80 cm and 100 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 40: 1, 2, 4, 5, 8, 10, 20, 40
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
The highest common factor of 40, 80 and 100 is 20.
Greatest possible length of each smaller piece of wire = 20 cm
(b)
Total length of wire
= 80 + 100 + 40
= 220 cm
Number of smaller pieces
= 220 ÷ 20
= 11
Answer(s): 20 cm; (b) 11