Mr. Nick has three pieces of string of length 150 cm, 210 cm and 270 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 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Factors of 210:1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
Factors of 270:1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The highest common factor of 150, 210 and 270 is 30.
Greatest possible length of each smaller piece of string = 30 cm
(b)
Total length of string
= 210 + 270 + 150
= 630 cm
Number of smaller pieces
= 630 ÷ 30
= 21
Answer(s): 30 cm; (b) 21