Mr. Julian has three pieces of thread of length 120 cm, 150 cm and 180 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 150:1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Factors of 180:1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The highest common factor of 120, 150 and 180 is 30.
Greatest possible length of each smaller piece of thread = 30 cm
(b)
Total length of thread
= 150 + 180 + 120
= 450 cm
Number of smaller pieces
= 450 ÷ 30
= 15
Answer(s): 30 cm; (b) 15