The sum of two numbers is 528 and their HCF i | vedclass

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

Question

(A) Let the two numbers be $33a$ and $33b$,where $a$ and $b$ are coprime numbers (i.e.,$gcd(a, b) = 1$).Given that the sum of the numbers is $528$,we

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) Let the two numbers be $33a$ and $33b$,where $a$ and $b$ are coprime numbers (i.e.,$gcd(a, b) = 1$).Given that the sum of the numbers is $528$,we have $33a + 33b = 528$.Dividing by $33$,we get $a + b = \frac{528}{33} = 16$.We need to find pairs $(a, b)$ such that $a + b = 16$ and $gcd(a, b) = 1$ (since $HCF$ is $33$): Possible pairs $(a, b)$ where $a Note: $(2, 14), (4, 12), (6, 10), (8, 8)$ are excluded because they have a common factor other than $1$.Thus,there are $4$ such pairs.

The sum of two numbers is $528$ and their $HCF$ is $33$. The number of pairs of numbers satisfying the above conditions is

Similar Questions

In a school,$391$ boys and $323$ girls have been divided into the largest possible equal classes,so that each class of boys numbers the same as each class of girls. What is the number of classes?

What is the $H.C.F.$ of $27, 18$ and $36$?

Two numbers are in the ratio $5:6$. If their $H.C.F.$ is $4$,then their $L.C.M.$ will be

$A$ 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.

Find the least number which when divided separately by $15, 20, 36$ and $48$ leaves $3$ as remainder in each case.

Vedclass Test Series

Exam Paper Generator

Online Exam Module