Mr. Jeremy has three pieces of thread of length 120 cm, 180 cm and 270 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 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 180:1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Factors of 270:1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The highest common factor of 120, 180 and 270 is 30.
Greatest possible length of each smaller piece of thread = 30 cm
(b)
Total length of thread
= 180 + 270 + 120
= 570 cm
Number of smaller pieces
= 570 ÷ 30
= 19
Answer(s): 30 cm; (b) 19