0

# How do you use prime factorization to find out how many factors it has?

Updated: 11/3/2022

Wiki User

14y ago

If you know the prime factorization of a number, you can determine the number of factors it has by looking at the possible combinations of the factors.

If the prime factorization of a number is p1a * p2b *p3c , then its factors (including one and the number itself) will p1i * p2j *p3k , with i a whole number between 0 and a, j a whole number between 0 and b, and k a whole number between 0 and c.There are (a+1) numbers that i can be, (b+1) numbers that j can be, and (c+1) numbers that k can be, so there are (a+1)*(b+1)*(c+1) factors (including one and the number itself).

It makes more sense using a concrete example:

Consider the number 360. We want to figure out how many factors it has.

It's prime factorization is 23*32*5. For a number to be a factor of 360, it will have to have only these prime factors, and the largest exponent the exponent can be for each of the factors is that factors exponent in the prime factorization of 360. So a factor of 360 will be a product of 2 (to the 0,1,2, or 3) power, 3 (to the 0,1, or 2), and 5 (to the 0 or 1 power). There are thus 4*3*2 = 24 factors of 360 (including 1 and 360). We can check this by systematically listing out the factors of 360:

20*30*50=1

20*30*51=5

20*31*50=3

20*31*51=15

20*32*50=9

20*32*51=45

21*30*50=2

21*30*51=10

21*31*50=6

21*31*51=30

21*32*50=18

21*32*51=90

22*30*50=4

22*30*51=20

22*31*50=12

22*31*51=60

22*32*50=36

22*32*51=180

23*30*50=8

23*30*51=40

23*31*50=24

23*31*51=120

23*32*50=72

23*32*51=360

Wiki User

14y ago

Earn +20 pts
Q: How do you use prime factorization to find out how many factors it has?
Submit
Still have questions?
Continue Learning about Math & Arithmetic

### How many factors are there is the prime factorization of 400?

Two distinct prime factors, six total prime factors.

### How many prime factorization of 147?

As a product of its prime factors: 3*7*7 = 147

### Where can I find prime factorization worksheets online?

You can find prime factorization worksheets at math world dot com. They have many to choose from and download and print for your convenience. Great site to use.

### What is the easiest way to find prime factorization?

Many people find factor trees to be the easiest.

### How many prime factorizations does every number have?

Every prime number has exactly 2 factors, 1 and the number itself.

Related questions

### How many factors are there is the prime factorization of 400?

Two distinct prime factors, six total prime factors.

### How many ways can you find the prime factorization of a number?

Divide it by each prime number which does not have remainder.

### How many prime factors of 48 are there?

There are 2 prime factors of 48. The prime factorization of 48 is: 24 x 3 = 48

### How do you find out the prime factor?

To find a prime factorization, divide a composite number and its factors by prime numbers until all the factors are prime. Many people find factor trees helpful in visualizing this process. Example: 210 210 Divide by two. 105,2 Divide by three. 35,3,2 Divide by five. 7,5,3,2 Stop. All the factors are prime. 2 x 3 x 5 x 7 is the prime factorization of 210.

### How many prime factorization of 147?

As a product of its prime factors: 3*7*7 = 147

### How many in factors in 156?

You can find out the number of factors of any number from its prime factorization by adding one to each exponent and multiplying. The prime factorization of 156 is 2^2 x 3^1 x 13^1 3 x 2 x 2 = 12 156 has 12 factors.

### How many factors does 420 have?

The prime factorization of 420 is: 2 &times; 2 &times; 3 &times; 5 &times; 7

### What is the prime factorization of0 and 48?

Zero has infinitely many factors, so a prime factorization would be unwieldy and ultimately meaningless. The prime factorization of 48 is 2 x 2 x 2 x 2 x 3

### How many longest strings of factors are there for a given number?

For composite numbers, only one string of factors is the longest; the prime factorization.

### Where can I find prime factorization worksheets online?

You can find prime factorization worksheets at math world dot com. They have many to choose from and download and print for your convenience. Great site to use.

### What is the easiest way to find prime factorization?

Many people find factor trees to be the easiest.

### How many prime numbers does 63 have?

3 and 7 are the two different prime factors of 63. Prime factorization of 63 is 3 x 3 x 7.