Can some one explain me this problem, i have the solution but i am having hard time understanding it.
if x=8y, where y is a prime number greater than 2,how many positive odd factors does y have?
Solution:
If y is a prime number greater than 2, it must be odd. Since 8=2x2x2, the only odd factor of x will be 1 and y itself.
Picking numbers works great here, getting us around the highly abstract "math solution." Say y=3. Then x=24. The only odd factors of 24 are 1 and 3.
x=8y (how many positive odd factors does y have?)
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Based on the answer, I guess the question should have been 'how many positive odd factors does X have?'
Try visualising the number X as a box in which its prime factors are jostling around. The box will have three 2's, one y. 'y' will be the only odd number.
1 is anyway a factor of all integers.
Hence, 1 and y are the only two +ve odd factors of X.
Hope this helps. Thanks.
Try visualising the number X as a box in which its prime factors are jostling around. The box will have three 2's, one y. 'y' will be the only odd number.
1 is anyway a factor of all integers.
Hence, 1 and y are the only two +ve odd factors of X.
Hope this helps. Thanks.
- eaakbari
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y is a prime number. How many factors does a prime number have?
Note that any prime number will have only 2 factors and no more, that is the number itself and 1.
For instance 7= 7*1
Also as a side note you should know that 2 is the only even prime
Back to the question
It asks you for odd factors of x. Always break these kind of questions into primes(prime factorization)
x = 8y
x = 2*2*2 *y*1
We know that 2 is even and y is odd and prime ans 1 is odd too. So it has precisely 2 odd factors, y and 1.
Note that any prime number will have only 2 factors and no more, that is the number itself and 1.
For instance 7= 7*1
Also as a side note you should know that 2 is the only even prime
Back to the question
It asks you for odd factors of x. Always break these kind of questions into primes(prime factorization)
x = 8y
x = 2*2*2 *y*1
We know that 2 is even and y is odd and prime ans 1 is odd too. So it has precisely 2 odd factors, y and 1.