Question

Find the greatest number which divides 228, 305 and 382, leaving remainders 3, 5 and 7 respectively.​

Answer 1

Answer:

75

Step-by-step explanation:

We know that

Dividend= (Quotient*Divisor)+Remainder

I,e.

Dividend-Remainder=Quotient*Divisor+0

The greatest number (the divisor) shall therefore divide (Dividend-Remainder) entirely, leaving no remainder

Hence, we need to find the HCF (Highest Common Factor) of

228-3= 225

305-5= 300

382-7= 375

I'm assuming you have already learnt prime factorization method, if not, here you go,

225=       3*5*5*3

300=2*2*3*5*5

375=        3*5*5*5

The HCF hence becomes the product of the numbers which are in all 3 expressions,i.e,3*5*5=75