Mr. Warren has three pieces of wire of length 210 cm, 240 cm and 300 cm. He wishes to cut the three pieces of wire into smaller pieces of equal length with no remainder.
- What is the greatest possible length of each of the smaller pieces of wire?
- How many of the smaller pieces of wire 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 240:1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
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, 240 and 300 is 30.
Greatest possible length of each smaller piece of wire = 30 cm
(b)
Total length of wire
= 240 + 300 + 210
= 750 cm
Number of smaller pieces
= 750 ÷ 30
= 25
Answer(s): 30 cm; (b) 25
