Find the Factors of Any Number and Learn Prime Factorization

How to Calculate Factors of a Number

You need to have good command on division and multiplication to calculate the factors of any number. Factors are the numbers that you get by multiplying other numbers. In other word, factors of a number are all the possible divisors.  Multiplication Tables are very useful to calculate factors and we even have a Multiplication Table Generator that you can use.

Find the Factors of Any Number Using this Factor Calculator

Note: Do not forget to click the Clear button to try another number.

It was the calculator and now let’s learn it how it is done.

Let’s solve some of the Factor Calculation related maths to understand.

Q: Find the Factors of 32

The factors will be the same as the divisors of the number.

Answer: 1, 2, 4, 8, 16, 32

Explanation: We will always include the number itself (that is 32 here) and 1 in the answer whenever we are asked to find the factors. So the first one is 1 x 32 that gives us the number 32. Now we have to try to find that number that can give us the number 32 by multiplying other numbers. However, only pick the unique numbers. For example, 4 x 8 gives us 32, so there is no need to write 8 x 4 again. Just use the unique numbers and all the unique numbers will be the factors of 32. That’s how we got 1, 2, 4, 8, 16, 32.

Q: What are the factors of 45?

Answer: 1, 3, 5, 9, 45

Explanation: As we explained in the first example. 1 and the number itself will always be included when we try to get the factors. Thereafter, we will find all unique numbers that give us the number 45 after multiplication. So we got 1, 3, 5, 9, 45 that are the factors of 45.

What are Prime Factors and How to Calculate Prime Factorization

Prime Factors and Prime Factorization Calculator

Let’s learn to do it without the help of any calculator because you should learn it how it is done instead of using a calculator than will have a bad impact on your educational system.

Before we go ahead to explain Prime Factors and Prime Factorization, you first need to know what the Prime Numbers are.

There are 2 types of numbers:

1. Prime Numbers
2. Composite Numbers

Prime Numbers:

The numbers that you can’t divide by any other numbers are known as prime numbers. You can divide these number only by 1 or the number itself, e.g. 41, 23, 11, 2 and there are many more.

Composite Numbers:

These numbers are kind of numbers that is divisible by other numbers, e.g. 9, 4, 6, 8, 12, 34, and many more.

What are Prime Factors  and Prime Factorization:

Prime numbers are the Prime Factors. So all the prime numbers that we get while calculating factors will be added as prime factors. We will now always try to find the lowest divisor of the number to get prime factors and we will skip number 1. You will understand better when you see solved examples.

Prime Factorization is about sorting the prime factors using exponents (a quantity representing the power).

Q: For example: Find the Prime Factors of 36 and perform Prime Factorization

Always try to get the lowest divisor first and you can keep trying dividing by the same number unless the number is not divisible anymore, then try another number.

 

Answer:

Prime Factors of 36 = 2 x 2 x 3 x 3
Prime Factorization =  2² x 3²

Try another example

Q: Find the Prime Factors of 40 and do Prime Factorization (Use Factor Tree Method):

Factor Tree Method: Follow the sequence shown in the image. We only take all the numbers of the left side as Prime Factor Numbers and we take the last number of the right side.

Answer:

Prime Factors of 40 = 2 x 2 x 2 x 5

Prime Factorization = 2³ x 5

Q: Perform a Prime Factorization of the number 91

So we are taking all the number from the left and the last number from the right.

Answer: 

Prime Factors: 7 x 13
Prime Factorization: 7 x 13

Both are same in this case because we do not have many divisors.

More Examples of Finding Factors

Q: Find the Factors of 18

Answer: 1, 2, 3, 6, 9, 18

Q: Get the Factors of 24

Answer: 1, 2, 3, 4, 6, 8, 12, 24

Q: Factors of 35

Answer: 1, 5, 7, 35

Q: Factors of 42

Answer: 1, 2, 3, 6, 7, 14, 21, 42

Q: Find the factors of 50

Answer: 1, 2, 5, 10, 25, 50

Q: Get the Factors of 54

Answer: 1, 2, 3, 6, 9, 18, 27, 54

Q: Find the factors of 68

Answer: 1, 2, 4, 17, 34, 68

Q: Factors of 72

Answer: 1, 2, 3, 4, 6, 8, 9, 12, 18, 26, 36, 72

Q: Get the Divisors or Factors of 90

Answer: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Q: What are the factors of 216

Answer: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

Q: Give me the Factors of 4

Answer: 1, 2, 4
(We will not include any duplicate number. So 2 cannot be mentioned 2 times).

Q: Find the Factors of 8

Answer: 1, 2, 4, 8

Q: Get the Factors of 15

Answer: 1, 3, 5, 15

Q: What are the Factors of 23

Answer: 1, 23

More Factors with Answer:

• Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
• Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
• Factors of 91: 1, 7, 13, 91
• Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
• Factors of 6: 1, 2, 3, 6
• Factors of 10: 1, 2, 5, 10
• Factors of 12: 1, 2, 3, 4, 6, 12
• Factors of 16: 1, 2, 4, 8, 16
• Factors of 20: 1, 2, 4, 5, 10, 20
• Factors of 21: 1, 3, 7, 21
• Factors of 25: 1, 5, 25
• Factors of 26: 1, 2, 13, 26
• Factors of 27: 1, 3, 9, 27
• Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
• Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
• Factors of 49: 1, 7, 49
• Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
• Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
• Factors of 63: 1, 3, 7, 9, 21, 63
• Factors of 64: 1, 2, 4, 8, 16, 32, 64
• Factors of 81: 1, 3, 9, 27, 81
• Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
• Factors of 89: 1, 89
• Factors of 91: 1, 7, 13, 91
• Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
• Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
• Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
• Factors of 145: 1, 5, 29, 145

Some More Prime Factorization Examples

Q: Get the Prime Factors of 144 and perform Prime Factorization

Answer:

Prime Factors: 2 x 2 x 2 x 2 x 3 x 3
Prime Factorization: 2⁴ x 3²

Q: Find the Prime Factors and perform Prime Factorization of 64

Answer:

Prime Factors: 2 x 2 x 2 x 2 x 2 x 2
Prime Factorization: 2⁶

Q: Calculate Prime Factors of Perform Prime Factorization of 30

Answer:

Prime Factors: 2 x 3 x 5
Prime Factorization: 2 x 3 x 5

Q: Calculate Prime Factors of Perform Prime Factorization of 16

Answer:

Prime Factors: 2 x 2 x 2 x 2
Prime Factorization: 2⁴