Question

find the greatest number which is divide by 742 and 1162 leaving 7 as a remainder.

Answer 1

742 is divided by 7 is 15 when 7 is remainder.
1162 is divided by 7 is 165 when 7 is remainder

Answer 2

Answer:

105

Step-by-step explanation:

This is a slight twist to the normal finds of the GCF of two numbers.

In this case, as a remainder of 7 is required, subtracting 7 from each number and then finding the GCF of the resulting numbers will solve the problem:

742 - 7 = 735

1162 - 7 = 1155

GCF of 1155 and 735 (using Euclid's method):

$\frac{1155}{735} = 1, remainder 420\\\\\frac{735}{420} = 1, remainder 315\\\\\frac{420}{315} = 1, remainder 105\\\\\frac{315}{105} = 3, remainder 0$

Hence, GCF of 735 & 1155 is 105, thus 105 is the greatest number that will divide 742 and 1162 leaving a remainder of exactly 7 each time.