Question

Find the largest positive integer that will divide 100, 245 and 343 leaving remainders 4, 5 and 7 respectively.

Answer 1

Given $100,245and343$ integers and leaving reminders $4,5and7$ respectively

Then number after deducting reminder are

$100-4=96$

$245-5=240$

and $343-7=336$

So largest positive integer is H.C.F of 9 $6,240.336$

Factors of $96=4\times 4\times 4$

Factorsof $240=4\times 4\times 3\times 5$

Factors of $336=4\times 4\times 3\times 7$

Then H.C F is $4\times 4\times 3=48$

Answer is $48$