What is the sum of all of the distinct, positive prime factors of 1260?

Question

PLZ HELP!!!!!

Answer 1

I. Factoring A Number Into Primes
1. Check to see if the first prime number, 2, divides evenly into the given number.

2. If it doesn't divide evenly, try the next prime number, 3. Continue until you find a prime factor.

3. Rewrite the given number as a product of the prime factor and the result from division.

4. Repeat steps 1-3 on the number resulting from division.

5. Repeat steps 1-4 until the given number is written as a product of primes.


1260/2 = 630
630/2=315
315/3=105
105/3=35
35/5=7
7/7=1

add all the denominators , 2+2+3+3+5+7 = 22

Answer 2

First factor the number.

1260 = 2 x 2 x 3 x 3 x 5 x 7

The distinct prime factors are 2, 3, 5, 7

Their sum is:

2 + 3 + 5 + 7 = 17

Answer 3

What you wanna find is known as using the function σ(n). In this case, you want to find σ(1260).

Your first step is to obtain the prime factorization of 1260.

1260 = 2 x 630 = 2 x 2 x 315 = 2 x 2 x 3 x 105 = 2 x 2 x 3 x 3 x 35
= 2 x 2 x 3 x 3 x 5 x 7

Now, what you want to do is change the prime factorization to use powers.

1260 = (2^2) (3^2) (5^1) (7^1)

We want to solve for σ(1260), so we take the σ of both sides, to get:

σ(1260) = σ((2^2) (3^2) (5^1) (7^1))
By another theorem, we can decomposite the single σ on the right hand side into multiple ones.

σ(1260) = σ(2^2)σ(3^2)σ(5^1)σ(7^1)

Remember that for any prime number, the factors are 1 and itself. That is
σ(p) = 1.

For any prime number to the power of m, know that
σ(p^m) = m + 1

That's what we apply in this case. We look at the *powers* of each prime factor, and then add 1 to it. So for this:

σ(1260) = σ(2^2)σ(3^2)σ(5^1)σ(7^1)

We get this

σ(1260) = (2 + 1)(2 + 1)(1 + 1)(1 + 1), or
σ(1260) = (3)(3)(2)(2) = 36

See what I did up there? I took the exponent of each prime number (respectively, 2, 2, 1, and 1), and then added 1 by the above theorem.

The general method to solve these types of questions is to obtain the prime factorization, give each prime number a power, and then remember the property that σ(p^m) = m + 1.

Edit: Oops; I answered your question incorrectly.
In this case, all you have to do is develop the prime factorization and then add all of them.

2 + 3 + 5 + 7 = 17

Answer 4

To do this problem, you should make a factor tree to find out what all of the prime factors of 1260 are. In this case, 1260 is 2x2x3x3x5x7. If you add those all up, you get 22. However, since you only want the distinct factors, you add up 2, 3, 5 and 7, for a total of 17.

Answer 5

First factor the number.

1260 = 2² * 3² * 5 * 7

The distinct prime factors are 2, 3, 5, 7

Their sum is:

2 + 3 + 5 + 7 = 17

Answer 6

You have lots of fine responses, with two different answers. You need to read you question very carefully and then read the answers very carefully to see which is correct.

The question asks you to sum the distinct, prime factors.

Answer 7

Factoring:
1260| 2
..630| 2
..315| 3
..105| 3
... 35| 5
......7| 7
......1
2².3².5.7 = 1260
4 + 6 + 5 + 7 = 22
The answer is 22.
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Answer 8

This site is useful:
http://www.math.wustl.edu/cgi-bin/primes

Answer 9

I believe it is twenty two