Question

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

Answer 1

Answer:

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

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

Answer :-

finding the difference first,

→ (228 - 3) = 225

→ (305 - 5) = 300

→ (382 - 7) = 375 .

now, prime factors of 225, 310 and 375 are :-

→ 225 = 3 * 3 * 5 * 5

→ 300 = 2 * 2 * 3 * 5 * 5

→ 375 = 3 * 5 * 5 * 5

finding HCF of difference now,

→ HCF = 3 * 5 * 5 = 75 .

Therefore, we can conclude that, the the greatest number which divides 228, 305 and 382 leaving remainders 3,5 and 7 respectively will be 75 .

Learn more :-

वह छोटी से छोटी संख्या बताईये जिसमे 7,9,11 से भाग देने पर 1,2,3 शेष बचे

https://brainly.in/question/9090122