When 1062, 1134 and 1182 are divided by the greatest number x, the remainder in each case is y. What is the value of (x - y)?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 18
Concept
We need to find HCF. HCF can be calculated by taking the difference of the numbers when they leave same remainder when divided by same number. When A, B and C are divided by a greatest number 'K' and leaves the same remainder each time, then the value of K can be calculated by (A - B) (B - C) and (A - C)
Application
We need to take the differences of each number to calculate HCF
= (1134 - 1062), (1182 - 1134) and (1182 - 1062)
1134 - 1062 = 72
1182 - 1134 = 48
1182 - 1062 = 120
Upon Prime Factorization
72 = 23 × 32
48 = 24 × 3
120 = 23 × 3 × 5
To calculate HCF, we need to take numbers which are common in each of the numbers
Thus we get = 23 x 3 = 24
Therefore, the greatest number or x = 24
When we divide 1134 by 24, we get remainder as 6 which is y
Therefore = x - y
= 24 - 6 = 18