How many factors does 36^2 have?
2
8
24
25
26
prime factorization tree comes to four 2's and four 3's. Trap is answe choice 8 but want a way to factor see concrete way.. I factored out fully and came to 24. MIssed something important.
qa is 25
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albertrahul
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netigen
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This is a permutation combination question
prime factors of 36 = 2 x 2 x 3 x 3
prime factors of 36^2 = 2 x 2 x 3 x 3 x 2 x 2 x 3 x 3
Now, the way to find all factors is to find all possible combinations
there are 4 2's and 4 3's,
so a 2 can occur from 0-4 times (5 possibilities) and similarly 3 can occur from 0-4 times
total combinations = 5x5 = 25
prime factors of 36 = 2 x 2 x 3 x 3
prime factors of 36^2 = 2 x 2 x 3 x 3 x 2 x 2 x 3 x 3
Now, the way to find all factors is to find all possible combinations
there are 4 2's and 4 3's,
so a 2 can occur from 0-4 times (5 possibilities) and similarly 3 can occur from 0-4 times
total combinations = 5x5 = 25
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VerbalAttack
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In fact there is a formula for this;
To find the number of factors (also called integral divisors) that a number has, increment the powers of the prime factors by 1 and then multiply them.
As for 36^2 = 2^4 * 3^4
The powers of the prime factors are 4 & 4. Apply the formula and you get (4+1) * (4+1) = 25.
Cheers
To find the number of factors (also called integral divisors) that a number has, increment the powers of the prime factors by 1 and then multiply them.
As for 36^2 = 2^4 * 3^4
The powers of the prime factors are 4 & 4. Apply the formula and you get (4+1) * (4+1) = 25.
Cheers
