Find the greatest number which will divide 25 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) To find the greatest number that leaves the same remainder when dividing $25, 73,$ and $97$,we calculate the differences between the numbers:$73 -

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(C) To find the greatest number that leaves the same remainder when dividing $25, 73,$ and $97$,we calculate the differences between the numbers:$73 - 25 = 48$$97 - 73 = 24$$97 - 25 = 72$Now,find the $H.C.F.$ of these differences: $48, 24,$ and $72$.The prime factorization of the numbers is:$48 = 2^4 	imes 3$$24 = 2^3 	imes 3$$72 = 2^3 	imes 3^2$The $H.C.F.$ is the product of the lowest powers of common prime factors: $2^3 	imes 3 = 8 	imes 3 = 24$.Thus,the greatest number is $24$.

Find the greatest number which will divide $25, 73$ and $97$ so as to leave the same remainder in each case.

Similar Questions

Find the least number which when divided by $2, 3, 4, 5$ and $6$ leaves $1, 2, 3, 4$ and $5$ as remainders,respectively,but when divided by $7$ leaves no remainder.

How many numbers are there from $300$ to $700$ which are divisible by $2, 3,$ and $7$?

Three numbers are in the ratio $3: 4: 5$ and their $LCM$ is $2400$. Their $HCF$ is

The $L.C.M.$ of two numbers is $120$ and their $H.C.F.$ is $10.$ Which of the following can be the sum of those two numbers?

The $LCM$ of $2^{2} \times 3^{2} \times 5 \times 11$,$2^{4} \times 3^{4} \times 5^{2} \times 7$,and $2^{5} \times 3^{3} \times 5^{2} \times 7^{2} \times 11$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module