Question

What is the greatest number that will divide 62, 78 and 109 leaving remainders 2, 3 and 4 respectively?

Answer 1

Get all the common factors of 62 − 2, 78 − 3 and 109 − 4, i.e., 60, 75 and 105 and see that the common factors will divide them all. [0.5 marks]
The greatest number is the H.C.F of 60, 75 and 105.
60=2 x 2 x 3 x 5
[0.5 marks]
75=3 x 5 x 5
[0.5 marks]
105=3 x 5 x 7
[0.5 marks]
Hence, the HCF is 3 x 5=15, which is the greatest number that will divide 62, 78, 109 leaving remainders 2, 3 and 4 respectively. [1 marks]