Mr. Paul has three pieces of string of length 120 cm, 180 cm and 300 cm. He wishes to cut the three pieces of string into smaller pieces of equal length with no remainder.
- What is the greatest possible length of each of the smaller pieces of string?
- How many of the smaller pieces of string 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 300:1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
The highest common factor of 120, 180 and 300 is 60.
Greatest possible length of each smaller piece of string = 60 cm
(b)
Total length of string
= 180 + 300 + 120
= 600 cm
Number of smaller pieces
= 600 ÷ 60
= 10
Answer(s): 60 cm; (b) 10