Mr. Cody has three pieces of string of length 350 cm, 400 cm and 500 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 350: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
Factors of 400:1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
Factors of 500:1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
The highest common factor of 350, 400 and 500 is 50.
Greatest possible length of each smaller piece of string = 50 cm
(b)
Total length of string
= 400 + 500 + 350
= 1250 cm
Number of smaller pieces
= 1250 ÷ 50
= 25
Answer(s): 50 cm; (b) 25