Question

find the largest number that will divide 220,313,and 716 leaving remainder 3 in each case?

Answer 1

217 = 7*31
310 = 10*31
713 = 23*31

It appears that dividing any of the original numbers by 31 will leave a remainder of 3.

Answer 2

220 - 3 = 217

313 - 3 = 310

716 - 3 = 713


Find the prime factorization of each integer.

217 = 7 ∙ 31

310 = 2 ∙ 5 ∙ 31

713 = 23 ∙ 31

The "Greatest Common Factor " is the largest of the common factors (of two or more numbers)

In this case GCF = 31

Because 31 is the greatest number that divides evenly into all of them.


The largest number that will divide 220,313,and 716 leaving remainder 3 = 31



220 / 31 = ( 217 + 3 ) / 31 = 217 / 31 + 3 / 31 = 7 + 3 / 31

A remainder = 3


313 / 31 = ( 310 + 3 ) / 31 = 310 / 31 + 3 / 31 = 10 + 3 / 31

A remainder = 3


716 / 31 = ( 713 + 3 ) / 31 = 713 / 31 + 3 / 31 = 23 + 3 / 31

A remainder = 3

Answer 3

31