Question

find the greatest number that will divide 76, 114, and 152 leaving the remainders 2,3 and 4 respectively.​

Answer 1

Answer:

Given:

Three numbers 76 and 114 and 152 are the remainder 2,3 and 4 respectively when divided by a number.

To Find:

Find the greatest number that will divide 76 and 114 and 152 leaving the remainder 2,3 and 4 respectively

Solution:

⇒ On dividing 76, the remainder is 2,

this means the number divides 76-2 =7476−2=74 exactly

⇒ Similarly, on dividing 114, the remainder is 3,

meaning the number divides 114 - 3 = 111114−3=111 exactly

⇒ Similarly, on dividing 152, the remainder is 4,

meaning the number divides 152 - 4 = 148152−4=148 exactly

So the number divided 76, 114 \ and \ 15276,114 and 152 exactly

Factors of 76 \ are \ 76 = 2 \times 2 \times 1976 are 76=2×2×19

Factors of 114 \ are \ 114 = 2 \times 3 \times 19114 are 114=2×3×19

Factors of 152 \ are \ 152 \ = 2 \times 2 \times 2 \times 19152 are 152 =2×2×2×19

So the greatest common factor is 2 \times 19 = 382×19=38

Hence the greatest number of such sort is 38