Question

Find greatest number which on dividing 34100 leaves remainder 63 and on dividing 307100 leaces remainder 93

Answer 1

Therefore the required number is 337.

Step-by-step explanation:

We know that,

Dividend = (Divisor × Quotient) + reminder.

⇒Dividend- reminder= (Divisor × Quotient)

Let the divisor be a.

Given that,  Dividend =34100 , reminder =63

∴Dividend- reminder= 34100-63 =34037=Divisor × Quotient

Again  Dividend =307100 , reminder =93

∴Dividend- reminder=307100-93 = 3070007=Divisor × Quotient

In both case the divisors are same.

To find the divisors, we have to find the g.c.d of 34037 and  3070007

34037=101×337

3070007=337×911

The g.c.d of  34037 and  3070007 is 337.

Therefore the required number is 337.