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If two positive integers a and b are written as a = x3y2 and b = xy3; x, y are prime numbers, then HCF (a, b) is
- a)xy
- b)xy2
- c)x3y3
- d)x2y2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If two positive integers a and b are written as a = x3y2and b = xy3; x...
Given, a = x^3y^2 and b = xy^3, where x and y are prime numbers.
To find: HCF (a, b)
Solution:
1. Prime factorization of a and b:
a = x^3y^2 = xxxyyy
b = xy^3 = xyyy
2. HCF of two numbers is the product of all the common prime factors raised to the lowest power.
3. Common prime factors in a and b are:
xyy
4. Product of all common prime factors raised to the lowest power:
xy^2
Therefore, HCF (a, b) = xy^2, which is option B.
Thus, the correct answer is Option B (xy^2).
To find: HCF (a, b)
Solution:
1. Prime factorization of a and b:
a = x^3y^2 = xxxyyy
b = xy^3 = xyyy
2. HCF of two numbers is the product of all the common prime factors raised to the lowest power.
3. Common prime factors in a and b are:
xyy
4. Product of all common prime factors raised to the lowest power:
xy^2
Therefore, HCF (a, b) = xy^2, which is option B.
Thus, the correct answer is Option B (xy^2).
Community Answer
If two positive integers a and b are written as a = x3y2and b = xy3; x...
Option But
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If two positive integers a and b are written as a = x3y2and b = xy3; x, y are prime numbers, then HCF (a, b) isa)xyb)xy2c)x3y3d)x2y2Correct answer is option 'B'. Can you explain this answer?
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