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

The $H.C.F.$ of two numbers is $12$ and their difference is $12$. The numbers are:

Find the greatest number that will divide $390, 495,$ and $300$ without leaving a remainder.

$A$ room is $4\, m\, 37\, cm$ long and $3\, m\, 23\, cm$ broad. It is required to pave the floor with minimum square slabs. Find the number of slabs required for this purpose.

Three pieces of timber $42 \ m$,$49 \ m$,and $63 \ m$ long have to be divided into planks of the same length. What is the greatest possible length of each plank (in $m$)?

In four consecutive prime numbers that are in ascending order,the product of the first three is $385$ and that of the last three is $1001$. The largest given prime number is

Vedclass Test Series

Exam Paper Generator

Online Exam Module