Mr. Henry has three pieces of thread of length 180 cm, 210 cm and 300 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 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Factors of 210:1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
Factors of 300:1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
The highest common factor of 180, 210 and 300 is 30.
Greatest possible length of each smaller piece of thread = 30 cm
(b)
Total length of thread
= 210 + 300 + 180
= 690 cm
Number of smaller pieces
= 690 ÷ 30
= 23
Answer(s): 30 cm; (b) 23