Question

Find the greatest number which divides the number 81,1411,2228 leaving the remainder 7,5,8 respectively...Please help​

Answer 1

Answer:

Step-by-step explanation:

Suppose the number is X

If we divide 1195 by X we get 7 as a reminder.

that means (1195-7)=1188 is divisible by X

Again,

If we divide 762 by X we get 6 as a reminder.

that means (762-6)=756 is divisible by X

As X is the highest number which can divide 1188 and 756 that means X is the HCF of 1188 and 756.

therefore,

Find the prime factorization of 1188

1188=2\times2\times3\times3\times3\times111188=2×2×3×3×3×11

and

Find the prime factorization of 756

756=2\times2\times3\times3\times3\times7756=2×2×3×3×3×7

To find the HCF, multiply all the prime factors common to both numbers:

Therefore, \text{HCF}=2\times2\times3\times3\times3=108HCF=2×2×3×3×3=108

108 is the greatest number which is dividing 1195 and 762 leaves remainder 7 and 6 respectively.