Problem on finding the greatest number

[burgess]

Help me to solve math homework problem

Find the greatest number which can divide 1356, 1868 and 2764 leaving the same remainder 12 in each case?

Thanks

[jackwilson]

Solve it with the help of HCF

[Guest]

Because there is a remainder.....subtract the remainder 12 from each given number first.......then find HCF of the numbers left after subtraction......and to find the HCF....find all the prime factors of each....then multiply together all the factors that are common......This gives the highest common factor......

[Guest]

Subtract 12 from each number gives 1344, 1856, 2752

Find the prime factors of these numbers, then multiply together all the factors that are common to each to find the Highest Common factor HCF ........ This works out to be .... 64

Check.....

1356/64 = 21 rem 12

1856/64 = 29 rem 12

2764/64 = 43 rem 12

So..... 64 is the biggest number that divides into each to leave a remainder of 12.

[burgess]

Thank you all for your replies