What is the sum of all the positive factors of 30?

Question

A. 70
B. 71
C. 72
D. 73
E. 74

Kinshook · Answer

Asked: What is the sum of all the positive factors of 30?

30 = 2*3*5

Sum of all positive factors of 30 = (1+2)(1+3)(1+5) = 3*4*6 = 72

IMO C

ElninoEffect · Answer

Prime factors of 30 are 5, 3 & 2.

So, the total number of factors of 30 can be found out which will be 8. ( Factors of 5 for 30 ) - This will be required to cross verify the number of factors we will be deriving.

Now factors of 30 - 1, 5, 3, 2, 6, 10, 15, 30 ( leads the number to 8, so we haven't missed anything.)

Now, add all of these sum will lead to "72".

Hence: 'C'

summerbummer · Answer

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Isn't this formula to also find out integral factors of 30?

MathRevolution · Answer

Method I: All positive factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

Sum: 72

Answer C

Method II: Find prime factors:  30 = 2^1 * 3^1 * 5^1

If N is a composite number and =  a^p*b^q*c^r …, where a, b, c are prime factors of N and p, q, r are positive integers, then the sum of all factors of N is equal to

(a^(p+1) -1)/(a-1) * (b^(q+1) -1)/(b-1) * (c^(e+1) -1)/(c-1) *….

Sum of prime factors:  \frac{2^2 - 1}{ 2-1} * \frac{3^2 - 1}{ 3-1} * \frac{5^2 - 1}{ 5-1}

=>  \frac{4 - 1}{1} * \frac{9 - 1 }{ 2} * \frac{25 - 1 }{ 4 }

=> 3 * 4 * 6 = 72

Answer C

Scuven · Answer

@kingshook what is the factors have an exponent (ex. 2^2 *3*5) Should we write (2^2+1)(3+1)(5+1)?

What is the sum of all the positive factors of 30?

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What is the sum of all the positive factors of 30?

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