Mr. Owen has three pieces of string of length 210 cm, 270 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 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
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 210, 270 and 300 is 30.
Greatest possible length of each smaller piece of string = 30 cm
(b)
Total length of string
= 270 + 300 + 210
= 780 cm
Number of smaller pieces
= 780 ÷ 30
= 26
Answer(s): 30 cm; (b) 26