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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)x4y3
- b)xy
- c)x2y3
- d)xy2
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If two positive integers a and b are written as a = x3y2 and b = xy3 ;...
It is given that,
a = x3y2 = x × x × x × y × y
b = xy3 = x × y × y × y
The HCF (Highest Common Factor) of two or more numbers is the highest number among all the common factors of the given numbers.
As HCF is the product of the smallest power of each common prime factor involved in the numbers.
HCF of a and b = HCF (x3y2, xy3)
= x × y × y
= xy2
Therefore,HCF (a, b) is xy2
Most Upvoted Answer
If two positive integers a and b are written as a = x3y2 and b = xy3 ;...
Correct option D because HCF is the highest common factor.So here in a and in b common factor are x and y and their HCF is x2y2.
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Community Answer
If two positive integers a and b are written as a = x3y2 and b = xy3 ;...
Solution:
Given, a = x4 y2 and b = x2 y3 where a and b are prime numbers.
We need to find HCF(a, b).
Calculating HCF:
HCF(a, b) = x2y2
Explanation:
To find the HCF of a and b, we need to find the common factors of a and b and then take the product of the highest power of each common factor.
Let's find the factors of a and b.
Factors of a are: x, x, x, x, y, y.
Factors of b are: x, x, y, y, y.
Common factors are: x, x, y, y.
Highest power of x: x2
Highest power of y: y2
Therefore, HCF(a, b) = x2y2.
Hence, the correct answer is option 'D'.
Given, a = x4 y2 and b = x2 y3 where a and b are prime numbers.
We need to find HCF(a, b).
Calculating HCF:
HCF(a, b) = x2y2
Explanation:
To find the HCF of a and b, we need to find the common factors of a and b and then take the product of the highest power of each common factor.
Let's find the factors of a and b.
Factors of a are: x, x, x, x, y, y.
Factors of b are: x, x, y, y, y.
Common factors are: x, x, y, y.
Highest power of x: x2
Highest power of y: y2
Therefore, HCF(a, b) = x2y2.
Hence, the correct answer is option 'D'.
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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) isa)x4y3b)xyc)x2y3d)xy2Correct answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If two positive integers a and b are written as a = x3y2 and b = xy3 ; x, y are prime numbers, then HCF (a, b) isa)x4y3b)xyc)x2y3d)xy2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two positive integers a and b are written as a = x3y2 and b = xy3 ; x, y are prime numbers, then HCF (a, b) isa)x4y3b)xyc)x2y3d)xy2Correct answer is option 'D'. Can you explain this answer?.
If two positive integers a and b are written as a = x3y2 and b = xy3 ; x, y are prime numbers, then HCF (a, b) isa)x4y3b)xyc)x2y3d)xy2Correct answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If two positive integers a and b are written as a = x3y2 and b = xy3 ; x, y are prime numbers, then HCF (a, b) isa)x4y3b)xyc)x2y3d)xy2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two positive integers a and b are written as a = x3y2 and b = xy3 ; x, y are prime numbers, then HCF (a, b) isa)x4y3b)xyc)x2y3d)xy2Correct answer is option 'D'. Can you explain this answer?.
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