Mr. Ian has three pieces of thread of length 80 cm, 100 cm and 200 cm. He wishes to cut the three pieces of thread into smaller pieces of equal length with no remainder.
- What is the greatest possible length of each of the smaller pieces of thread?
- How many of the smaller pieces of thread 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 200:1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
The highest common factor of 80, 100 and 200 is 20.
Greatest possible length of each smaller piece of thread = 20 cm
(b)
Total length of thread
= 100 + 200 + 80
= 380 cm
Number of smaller pieces
= 380 ÷ 20
= 19
Answer(s): 20 cm; (b) 19