i would say 25..
36^2 cab be written as 3^4* 2^4
hence the number of factors are (4+1) * (4+1) = 25..
let me know the OA.
factors
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sudhir3127
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parallel_chase
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There is rule to find the factors of any integer.
Suppose you need to find the number of factors for 20
First prime factorize
20 = 2*2*5 = 2^2 * 5^1
now just look at the exponents of two prime factors, you add 1 to each power and then multiply with each other
(2+1)*(1+1) = 3*2= 6
20 has 6 factors
1,2,4,5,10,20.
Similarly for 36^2 = 2^4 * 3^4
(4+1)*(4+1) = 5*5 =25
Hope its clear now.
Suppose you need to find the number of factors for 20
First prime factorize
20 = 2*2*5 = 2^2 * 5^1
now just look at the exponents of two prime factors, you add 1 to each power and then multiply with each other
(2+1)*(1+1) = 3*2= 6
20 has 6 factors
1,2,4,5,10,20.
Similarly for 36^2 = 2^4 * 3^4
(4+1)*(4+1) = 5*5 =25
Hope its clear now.
Great trick-thanks for that! Is there a similar trick if it were to ask for prime factors only?parallel_chase wrote:There is rule to find the factors of any integer.
Suppose you need to find the number of factors for 20
First prime factorize
20 = 2*2*5 = 2^2 * 5^1
now just look at the exponents of two prime factors, you add 1 to each power and then multiply with each other
(2+1)*(1+1) = 3*2= 6
20 has 6 factors
1,2,4,5,10,20.
Similarly for 36^2 = 2^4 * 3^4
(4+1)*(4+1) = 5*5 =25
Hope its clear now.
