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2 pieces of copper pipe 315 cm and 225 cm long will be cut into sections. All sections must have equal length. What is the greatest possible length per section?

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1 Answer

Similar type of problem but instead of listing all the possible factors we'll divide both by 5
315/5 = 63
225/5 = 45
 
Now we can find the greatest common factor of 45 and 63:
Factors of 45:1,3,5,9,15,45
Factors of 63:1,3,7,9,21,63
 
The GCF of those numbers is 9.  If we multiply that number by 5 (since we divided by 5 in the first step), we will find the GCF of 315 and 225 is 9*5 or 45
 
The greatest possible length per section is 45 (315/45 = 7, 225/45 = 5)