Question

find the greatest no which divide 510 and 986 leaving remainder 6 in each case.​

Answer 1

$\textbf{Given:}$

$\textsf{Numbers are 510 and 986}$

$\textbf{To find:}$

$\textsf{The greatest number which divide 510 and 986 leaving remainder 6}$

$\textbf{Solution:}$

$\textsf{Here, we have to find greatest common divisor of 510-6 and 986-6}$

$\textsf{That is, we have to find the G.C.D of 504 and 980}$

$\textsf{We find the G.C.D by prime factorization method}$

$\mathsf{504=2{\times}252}$

$\mathsf{504=2{\times}2{\times}126}$

$\mathsf{504=2{\times}2{\times}2{\times}63}$

$\mathsf{504=2^3{\times}3^2{\times}7}$.......(1)

$\mathsf{and}$

$\mathsf{980=2{\times}490}$

$\mathsf{980=2{\times}2{\times}245}$

$\mathsf{980=2^2{\times}5{\times}49}$

$\mathsf{980=2^2{\times}5{\times}7^2}$......(2)

$\textsf{Choose the common factors from (1) and (2), we get}$

$\mathsf{G.C.D=2^2{\times}7}$

$\implies\boxed{\mathsf{G.C.D=28}}$

$\textbf{Answer:}$

$\textsf{The greatest number whiich number 510 and 986 leaving remainder is 28}$

$\textbf{Find more:}$

Find the greatest number that divides 3128 and 420 ​

https://brainly.in/question/15327150

Find hcf of 144, 96, 54 by prime factorisation

https://brainly.in/question/2132704

Find the HCF of 252525 and 363636​

https://brainly.in/question/11206176

Find the largest number which divides 1280 and 1371 leaving a remainder 6 in each case

https://brainly.in/question/10102736

Answer 2

Given :

n₁ = 510

n₂ = 986

remainder = 6

To find :

The greatest number which is divide 510 and 986 leaving remainder 6 in each case.

Solution :

First subtract 6 from 510 and 986.

⇒ 510 - 6 = 504

⇒ 986 - 6 = 980

Then find the HCF. To find the HCF first find the prime factorization of both the numbers.

Prime factorization of 504 = 2 x 2 x 2 x 3 x 3 x 7

Prime factorization of 980 = 2 x 2 x 5 x 7 x 7

Now take out the common factors from both the numbers.

⇒ 2 , 2 , 7

x = 2 × 2 × 7

x =  28

28 is the greatest number which will divide 510 and 986 leaving remainder 6 in each case.