Question

find the greatest number which divide 228 305 and 382 leaving remainder 3 5 and 7 respectively

Answer 1

The question is to find the H.C.F ( G.C.D)

Subtract the remainders from the respective numbers:
228-3 = 225
305-5 = 300
382-7 = 375
Now find the hcf of 225,300,375 and it will be the greatest number that divides 228,305 and 382 to leave respective remainders

225 = 15*15 = 3*3*5*5
300= 5*60 = 5*5*12= 5*5*3*2*2
375 = 5*75 = 5*5*5*3
Hence HCF(GCD) is 5*5*3 = 75 [two 5's and one 3 is common to all numbers]
Hence 75 is the greatest number which divides 228,305 and 382 to leave remainders 3,5,7 respectively.
Hope this helps

Answer 2

subtract all from remainders

that should be 225,300,375

find lcm

225_2*3*5*5

300_2*3*2*5*5

375_3*5*5*5

common.. 3*5*5

that's 75

thank u