Question

1.
Find the largest number that will divide 113, 135 and
160 leaving remainder 5, 3 and 4, respectively.​

Answer 1

Answer:

113 divided by the number leave 5 as remainder. so , the number divides 113 - 5 = 108 exactly

135 divided by the number leave 3 as remainder . so, the number divides 135 - 3 =132 exactly

160 divided by the number leave 4 as remainder. so, the number divides 160 - 4 =156

The greatest number that will divide 108 ,132 and 156 exactly is their HCF

108 = 2×2×3×3×3

132 =2×2×3×11

156 =2×2×3×13

HCF =2×2× 3

= 12

Answer 2

Answer:

The number divides 399,434 and 537 leaving the remainder 8,9 and 10.

So, that number will divide (399−8),(434−9) and (537−10) completely.

Now, the greatest number that will divide 391,425 and 527 completely, is the H.C.F. of these numbers.

391=17×23

425=5×5×17

527=17×31

H.C.F. =17