Question

let n is the gretest number that will be divide 1305, 4665 and 6905 leaving the same reminder in each case. that sum of digit in n is​

Answer 1

Answer ◆ 4

Let remainder is X

So 1305-X is divisible by N

Similarly

4665-X and 6905 -X are divisible by N.

Now

(6905 -X) - ( 4665-X) = 2240

is divisible by N

Example - if 49 is divisible by 7

————— 28 is divisible by 7

———- then 49–28 =21 is divisible by 7

Similarly

(4665-X)-(1305-X) = 3360

HCF of 2240 and 3360 is 1120

So Value of N is 1120

Sum of digits of N is 4 (1+1+2+0)

∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆

Verification

1120) 1305( 1

——-1120

———185

●●●●●●●●●●●●●●●●●●●●●●●●●●●●

1120)4665( 4

——4480

———185

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

1120)6905(6

——-6720

———185

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