|
Question 443306: How many factors does 29160 have?
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! This won't be fun, but it will be easier than listing all the factors of 29160.
===========================
Here's what I suggest:
Start by dividing it by 2 til you can't anymore:
29160 /2 = 14580 /2 = 7290 /2 = 3645
Now start dividing by 3:
3645 / 3 = 1215 /3 = 405 / 3 = 135 / 3 = 45 /3 = 15 /3 = 5
Now start dividing by 5:
5 /5 = 1
You would divide by (7,11,13 ... all primes) until you got down to 1, but since we got down to 1 after 5, then there would be no need.
=======================================
So we divided by 2 thrice, 3 6 times, and 5 once
Then the factorization is 
This is called the prime factorization of a number. Every number has a prime factorization except for 1.
There is a formula for finding the number of factors.
Number of factors for p^n = 
Also, the factors of pq = factors of p * factors of q.
Knowing these things, we can find the number of factors.
Factors of 29160 = factors(2^3) * factors(3^6) * factors(5)
Factors of 29160 = 
29160 has 56 factors.
=================
To summarize:
-
Find the prime factorization of a number.
Find the number of factors for each p^n, where p is a prime.
Multiply the number of factors you find in each to get your total number of factors.
Those 56 factors are:
1 2 3 4 5 6 8 9 10 12 15 18 20 24 27 30 36 40 45 54 60 72 81 90 108 120 135 162 180 216 243 270 324 360 405 486 540 648 729 810 972 1080 1215 1458 1620 1944 2430 2916 3240 3645 4860 5832 7290 9720 14580 29160
|
|
|
| |
