Question

it is known that 2726, 4472, 5054, 6412 have the same remainder when they are divided by some two digit number n find n​

Answer 1

The two digit number n=97

Step-by-step explanation:

Let x be the two digit number that divides the each given number and leaves same remainder.

Euclid algorithm

$a=bq+r$

Where $0\leq r<b$

Where a=Dividend

b=Divisor

q=Quotient

r=Remainder

By using Euclid algorithm

$2726=bx+r$..(1)

$4472=ax+r$..(2)

$5054=cx+r$...(3)

$6412=dx+r$....(4)

Subtract equation (1) from 2 , equation (2) from equation(3), equation (3) from equation (4) and equation (1) from equation (4)

$1746=(a-b)x$..(5)

$582=(c-a)x$

$1358=(d-c)x$

$3686=(d-a)x$

$1746=2\times 3\times 3\times 97$

$582=2\times 3\times 97$

$1358=2\times 7\times 97$

$3686=2\times 19\times 97$

97 is that number in which two digit and divides each number and leaves remainder 10.

Hence, the two digit number n=97

#Learns more:

https://brainly.in/question/1253938