MGMAT CAT:Change in number of factors when squaring a number

[ReQ]

How many factors does 36^2 have?

I can see there ought be be a relation between the fact that squaring will double the prime factors of a number and I ought to be able to figure out some relation between that and the resulting factors. But I can't figure one out off hand...

[manasi_sh]

HI
WELL SEE..IF YOU SQUARE 36 YOU WILL GET 1296 AND 1296 HAS 9 FACTORS. BUT THIS CAN BE LENGTHY.
THE EASIER WAY IS TO ADD ONE TO THE POWER(IN THIS CASE 2)= 2+1=3
AND THEN SQUARE THE RESULTANT NUMBER= 3^2= 9.
HOPE U UNDERSTOOD..

[Neo2000]

How many factors does 36^2 have?

I can see there ought be be a relation between the fact that squaring will double the prime factors of a number and I ought to be able to figure out some relation between that and the resulting factors. But I can't figure one out off hand...

Break down 36 into its Prime Components
36 = (2^2)x(3^2)
36^2 = 2^4 x 3^4

Number of Factors = (4+1)x(4+1) = 5x5 = 25

[ReQ]

How many factors does 36^2 have?

I can see there ought be be a relation between the fact that squaring will double the prime factors of a number and I ought to be able to figure out some relation between that and the resulting factors. But I can't figure one out off hand...

Break down 36 into its Prime Components
36 = (2^2)x(3^2)
36^2 = 2^4 x 3^4

Number of Factors = (4+1)x(4+1) = 5x5 = 25

Ahh thanks, got as far as the second to last line but couldn't remember the relation between how the number of factors related to the multiples of each prime.