Question

Find largest number which divides 1230 and 1926 leaving remainder 12 in each case

Answer 1

Solution:

The largest number when divides 1230 and 1926 leaving

remainder 12 ,

that number divides 1230-12

= 1218

and

1926 -12 = 1914 without leaving any remainder .

The largest number is the G.C.D

of 1218 and 1914

Now ,

Finding prime factors:

1218 = 2×3×29×7

1914 = 2×3×29×11

GCD of 1218 and 1914

= 2×3×29

= 174

Therefore,

Largest number which divides 1230 and 1926 leaving remainder 12 in each case is 174.

••••

Answer 2

Answer:

the HCF of 1218 and 1914 is 174

the required number is 174

Step-by-step explanation:

the required number is the HCF of the number

1230 -12 = 1218

1926 -12 = 1914

first we find the HCF of 1218 & 1914

by euclid's division algorithm

1914 = 1218 × 1 + 696

reminder 696 is not equal to 0

again using algorithm

1218 = 696 × 1 + 522 ( 522 is not equal to 0 )

696 = 522 × 1 + 174 ( 174 is not equal to 0 )

522 = 174 × 3 + 0. ( the reminder is 0 )

therefore the HCF of 1218 and 1914 is 174

hence the required number is 174