1. If two positive integers a and b are written as a = x3y2 and b = xy3; where x, y are prime numbers, then HCF (a,b) is: a) xy b) xy2 c) x3y3 d) x2y2
Question
- If two positive integers a and b are written as a = x3y2 and b = xy3; where x, y are prime numbers, then HCF (a,b) is: a) xy b) xy2 c) x3y3 d) x2y2
Solution
The Highest Common Factor (HCF) is calculated by taking the lowest powers of common factors.
In this case, the common factors are x and y.
For a = x^3y^2, the powers of x and y are 3 and 2 respectively.
For b = xy^3, the powers of x and y are 1 and 3 respectively.
So, the HCF will be x^1y^2 (taking the lowest powers of x and y), which corresponds to option b) xy^2.
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