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# What is the sum of the different positive prime factors of 1092?

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Math Expert
Joined: 02 Sep 2009
Posts: 44319
What is the sum of the different positive prime factors of 1092? [#permalink]

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12 Nov 2014, 10:12
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Tough and Tricky questions: Number Properties.

What is the sum of the different positive prime factors of 1092?

A. 5
B. 12
C. 20
D. 25
E. 27

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Joined: 29 Sep 2014
Posts: 15
Re: What is the sum of the different positive prime factors of 1092? [#permalink]

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12 Nov 2014, 11:05
First, we make a prime factorization by dividing 1096 by 2 then 3, etc.
1096=2^2*3*7*13
2*2+3+7+13=27

Is there a smartest way to solve this problem?
Manager
Joined: 21 Jul 2014
Posts: 127
Re: What is the sum of the different positive prime factors of 1092? [#permalink]

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12 Nov 2014, 11:25
gillesalex07 wrote:
First, we make a prime factorization by dividing 1096 by 2 then 3, etc.
1096=2^2*3*7*13
2*2+3+7+13=27

Is there a smartest way to solve this problem?

Agree with gillesalex07

The image below is an example of a factorization tree that might make it simpler to do the dividing quickly and with minimal error.

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Re: What is the sum of the different positive prime factors of 1092? [#permalink]

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12 Nov 2014, 12:26
3
KUDOS
I think answer is D: 25

The question is: What is the sum of the different positive prime factors of 1092?

1092 = 2^2*3*7*13

Sum of the DIFFERENT positive prime factors = 2 + 3 + 7 + 13 = 25
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Re: What is the sum of the different positive prime factors of 1092? [#permalink]

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12 Nov 2014, 13:14
pqhai wrote:
I think answer is D: 25

The question is: What is the sum of the different positive prime factors of 1092?

1092 = 2^2*3*7*13

Sum of the DIFFERENT positive prime factors = 2 + 3 + 7 + 13 = 25

Agreed - I sped through this at first and had the wrong answer until I re-read the question.
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Re: What is the sum of the different positive prime factors of 1092? [#permalink]

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12 Nov 2014, 20:02
gillesalex07 wrote:
First, we make a prime factorization by dividing 1096 by 2 then 3, etc.
1096=2^2*3*7*13
2*2+3+7+13=27

Is there a smartest way to solve this problem?

Original question has 1092
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Re: What is the sum of the different positive prime factors of 1092? [#permalink]

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12 Nov 2014, 20:04
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$$1092 = 2^2 * 3^1 * 7^1 * 13^1$$

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Re: What is the sum of the different positive prime factors of 1092? [#permalink]

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13 Nov 2014, 09:18
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Expert's post
Bunuel wrote:

Tough and Tricky questions: Number Properties.

What is the sum of the different positive prime factors of 1092?

A. 5
B. 12
C. 20
D. 25
E. 27

Kudos for a correct solution.

Official Solution:

What is the sum of the different positive prime factors of 1092?

A. 5
B. 12
C. 20
D. 25
E. 27

The question asks for the sum of the different prime factors of 1092.

The first step is to find the prime factorization of 1092. Since the last two digits of 1092 are divisible by 4 ($$92 = 80 + 12 = 4 \times 23$$), we can start by dividing 1092 by 4, giving us $$1092 \div 4 = 273$$. Since 4 is equal to $$2 \times 2$$, 1092 has two factors of 2.

Now, note that the digits of 273 add up to 12, which means that 3 is one of its factors: $$273 \div 3 = 91$$.

The prime factors of 91 are 7 and 13 (there is no easy divisibility rule for 7).

So the prime factorization of 1092 is: $$1092 = 2 \times 2 \times 3 \times 7 \times 13$$.

Now take the sum of the different factors: $$2 + 3 + 7 + 13 = 25$$.

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Re: What is the sum of the different positive prime factors of 1092? [#permalink]

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13 Nov 2014, 09:26
Looks like I missed an important word in the question. Good catch on "Different" prime factors. I agree that the answer is D.
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Re: What is the sum of the different positive prime factors of 1092? [#permalink]

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03 Sep 2017, 03:24
Sum of all prime factors would be:

2+2+3+7+13= 27

But sum of distinct/different factors would be:

2+3+7+13= 25

Sum of all factors of 1092 would be:
(2^3 - 1)(3^2 -1)(7^2 -1)(13^2-1) divided by (2-1)(3-1)(7-1)(13-1)

=7*8*48*168 divided by 1*2*6*12
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Re: What is the sum of the different positive prime factors of 1092?   [#permalink] 03 Sep 2017, 03:24
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