CAT Exam > CAT Questions > A number N when factorised can be written as ...
Start Learning for Free
A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. Find the number or perfect squares which are factors of N. (the three prime numbers P1, P2, P3 > 2)?
Most Upvoted Answer
A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. F...
Approach:
To find the number of perfect squares which are factors of N, we need to consider the powers of prime factors of N. A perfect square has an even power of its prime factors. Therefore, we need to find the number of combinations of even powers of P1, P2, and P3 that can be formed.
Solution:
Given, N = P1^4 x P2^3 x P3^7
Let the power of P1 be even, i.e., 0, 2, or 4
Let the power of P2 be even, i.e., 0 or 2
Let the power of P3 be even, i.e., 0, 2, 4, 6 or 7
Therefore, the possible combinations of even powers of P1, P2, and P3 are:
For P1, there are 3 possible even powers: 0, 2, and 4
For P2, there are 2 possible even powers: 0 and 2
For P3, there are 3 possible even powers: 0, 2, and 4
Hence, the total number of combinations of even powers of P1, P2, and P3 is:
3 x 2 x 3 = 18
Therefore, there are 18 perfect squares that are factors of N.
Answer:
The number of perfect squares which are factors of N is 18.
To find the number of perfect squares which are factors of N, we need to consider the powers of prime factors of N. A perfect square has an even power of its prime factors. Therefore, we need to find the number of combinations of even powers of P1, P2, and P3 that can be formed.
Solution:
Given, N = P1^4 x P2^3 x P3^7
Let the power of P1 be even, i.e., 0, 2, or 4
Let the power of P2 be even, i.e., 0 or 2
Let the power of P3 be even, i.e., 0, 2, 4, 6 or 7
Therefore, the possible combinations of even powers of P1, P2, and P3 are:
For P1, there are 3 possible even powers: 0, 2, and 4
For P2, there are 2 possible even powers: 0 and 2
For P3, there are 3 possible even powers: 0, 2, and 4
Hence, the total number of combinations of even powers of P1, P2, and P3 is:
3 x 2 x 3 = 18
Therefore, there are 18 perfect squares that are factors of N.
Answer:
The number of perfect squares which are factors of N is 18.
Community Answer
A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. F...
N = P1^a + P2^b + P3^c
Allowed values of a,b,c for N to be a perfect square :-
a = { 0,2,4 }
b = { 0,2 }
c = { 0,2,4,6 }
combinations of these sets values.
Ans = 3*2*4 = 24
Allowed values of a,b,c for N to be a perfect square :-
a = { 0,2,4 }
b = { 0,2 }
c = { 0,2,4,6 }
combinations of these sets values.
Ans = 3*2*4 = 24
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. Find the number or perfect squares which are factors of N. (the three prime numbers P1, P2, P3 > 2)?
Question Description
A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. Find the number or perfect squares which are factors of N. (the three prime numbers P1, P2, P3 > 2)? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. Find the number or perfect squares which are factors of N. (the three prime numbers P1, P2, P3 > 2)? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. Find the number or perfect squares which are factors of N. (the three prime numbers P1, P2, P3 > 2)?.
A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. Find the number or perfect squares which are factors of N. (the three prime numbers P1, P2, P3 > 2)? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. Find the number or perfect squares which are factors of N. (the three prime numbers P1, P2, P3 > 2)? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. Find the number or perfect squares which are factors of N. (the three prime numbers P1, P2, P3 > 2)?.
Solutions for A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. Find the number or perfect squares which are factors of N. (the three prime numbers P1, P2, P3 > 2)? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. Find the number or perfect squares which are factors of N. (the three prime numbers P1, P2, P3 > 2)? defined & explained in the simplest way possible. Besides giving the explanation of
A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. Find the number or perfect squares which are factors of N. (the three prime numbers P1, P2, P3 > 2)?, a detailed solution for A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. Find the number or perfect squares which are factors of N. (the three prime numbers P1, P2, P3 > 2)? has been provided alongside types of A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. Find the number or perfect squares which are factors of N. (the three prime numbers P1, P2, P3 > 2)? theory, EduRev gives you an
ample number of questions to practice A number N when factorised can be written as N = P1^4 x P2^3 x P3^7. Find the number or perfect squares which are factors of N. (the three prime numbers P1, P2, P3 > 2)? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup