What is the prime factors of 78

Why is the prime factorization of 78 written as 21 x 31 x 131?

What is prime factorization?

Prime factorization or prime factor decomposition is the process of finding which prime numbers can be multiplied together to make the original number.

Finding the prime factors of 78

To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.

If it doesn't make sense yet, let's try it...

Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let's start by dividing 78 by 2

78 ÷ 2 = 39 - No remainder! 2 is one of the factors!
39 ÷ 2 = 19.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
39 ÷ 3 = 13 - No remainder! 3 is one of the factors!
13 ÷ 3 = 4.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
13 ÷ 5 = 2.6 - This has a remainder. 5 is not a factor.
13 ÷ 7 = 1.8571 - This has a remainder. 7 is not a factor.
13 ÷ 11 = 1.1818 - This has a remainder. 11 is not a factor.
13 ÷ 13 = 1 - No remainder! 13 is one of the factors!

The orange divisor(s) above are the prime factors of the number 78. If we put all of it together we have the factors 2 x 3 x 13 = 78. It can also be written in exponential form as 21 x 31 x 131.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 78.

	78
2		39
	3		13

More Prime Factorization Examples

Try the factor calculator

Given #78# to factorise

• #78# ends with an even digit, so is divisible by #2# and we find:
  #78 = 2 * 39color(white)(0/0)#

• #39# ends with an odd digit, so is not divisible by #2#.

• The digits of #39# add up to a multiple of #3#, namely #3+9 = 12#. So we can tell that #39# is divisible by #3#:
  #39 = 3 * 13color(white)(0/0)#

• #13# is a prime number, not divisible by any number greater than #1# or less than #13#.

So the prime factorisation of #78# is:

#78 = 2 * 3 * 13#

This can also be represented by a factor tree:

#color(white)(0000)78#
#color(white)(000)"/"color(white)(00)"\"#
#color(white)(00)2color(white)(000)39#
#color(white)(00000)"/"color(white)(00)"\"#
#color(white)(0000)3color(white)(000)13#

Explanation:

As the last digit is #8# and even number, #78# is divisible by #2#

and as sum of the digits is #15# divisible by #3#, #78# is divisible by #3#

Dividing by #2# we get #39# and dividing #39# by #3#, we get #13#, a rime number.

Hence, prime factorization of #78# is #78=2xx3xx13#

Prime factors of 78

Prime factors of 78 :

In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly. The prime factorization of a positive integer is a list of the integer's prime factors, together with their multiplicities; the process of determining these factors is called integer factorization. Type the number in the input box below to find the prime factors of that number.

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Here we have a collection of all the information you may need about the Prime Factors of 78. We will give you the definition of Prime Factors of 78, show you how to find the Prime Factors of 78 (Prime Factorization of 78) by creating a Prime Factor Tree of 78, tell you how many Prime Factors of 78 there are, and we will show you the Product of Prime Factors of 78.

Prime Factors of 78 definition
First note that prime numbers are all positive integers that can only be evenly divided by 1 and itself. Prime Factors of 78 are all the prime numbers that when multiplied together equal 78.

How to find the Prime Factors of 78
The process of finding the Prime Factors of 78 is called Prime Factorization of 78. To get the Prime Factors of 78, you divide 78 by the smallest prime number possible. Then you take the result from that and divide that by the smallest prime number. Repeat this process until you end up with 1.

This Prime Factorization process creates what we call the Prime Factor Tree of 78. See illustration below.

All the prime numbers that are used to divide in the Prime Factor Tree are the Prime Factors of 78. Here is the math to illustrate:

78 ÷ 2 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1

Again, all the prime numbers you used to divide above are the Prime Factors of 78. Thus, the Prime Factors of 78 are:

2, 3, 13.

How many Prime Factors of 78?
When we count the number of prime numbers above, we find that 78 has a total of 3 Prime Factors.

Product of Prime Factors of 78
The Prime Factors of 78 are unique to 78. When you multiply all the Prime Factors of 78 together it will result in 78. This is called the Product of Prime Factors of 78. The Product of Prime Factors of 78 is:

2 × 3 × 13 = 78

Prime Factor Calculator
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Prime Factors of 79
We hope this step-by-step tutorial to teach you about Prime Factors of 78 was helpful. Do you want a test? If so, try to find the Prime Factors of the next number on our list and then check your answer here.

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