What is the prime factorization for 60

One of the methods to check the Prime Factor of a number is trial division. Trial division consists of very easy and basic algorithms, though it is an extremely slow process. In this method, we have to check each number by dividing the composite number in question by the integer and deciding if, and how many times, the number can divide the number equally.

Inhaltsverzeichnis Show

What are the Factors of 60?
How to Find the Factors of 60?
Pair Factors of 60
Prime Factorization of 60
Video Lesson on Prime Factors
Get Factors of More Numbers Here

To get the prime factorisation of 60, we have to start with dividing it by primes

60 ÷ 30 = 2

30 ÷ 15 = 2

15 ÷ 5 = 3

5 ÷ 1 = 5

So here he prime factorisation of 60 = 2 x 2 x 3 x 5 = 22 x 31 x 51

We can check it in a prime factorisation calculator also. The algorithm used in the calculator and trial division may differ but the result is always the same.

Factors of 60 are the pair of numbers which when multiplied together give the original number. In other words, we can say that, if any number divides 60 completely, then it is the factor of it. Also, as 60 is a composite number, we can derive its prime factors. Apart from 60, there are other numbers such as 24, 12, 18, 12, 48, etc which are composite in nature and have factors of more than 2. The multiples of 60 are the extended times of 60, such as 60, 120, 180, 240, 300, 360, 420, 480, 540 and so on. We can find the factors of a number by the simple multiplication method. It involves the multiplication of a pair of numbers to get another number, say 60. These pair of numbers are the factors. Let us find the factors in pairs for 60, here in this article.

Table of Contents:

What are the Factors of 60?

The factors of 60 are the numbers that are multiplied in pairs resulting in the number 60. In other words, the numbers that divide 60 exactly are the factors of 60. The number 60 has more than two factors, as it is a composite number. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60

Prime Factorization of 60: 2 × 2 × 3 × 5 or 22 × 3 × 5

How to Find the Factors of 60?

The steps to find the factors for 60 are given below:

Step 1: First, write the number 60 in your notebook.

Step 2: Find the two numbers, which on multiplication give 60, say 1 and 60, such as 1 × 60 = 60.

Step 3: Let us write another pair of numbers that gives 60 on multiplication, such as 2 and 30, i.e. 2 × 30 = 60.

Step 4: We know that 2 is a prime number with only two factors, i.e. 1 and the number itself. So, we cannot factorize it further.

2 = 1 × 2

Step 5: Now, we need to write another pair such as 3 and 20, i.e. 3 × 20 = 30

Here, 3 is a prime number so we cannot factorise it further.

Step 6: Similarly, we can write other factors as:

4 × 15 = 60

5 × 12 = 60

6 × 10 = 60

12 × 5 = 60

Here, the numbers are repeated in pairs.

Step 7: Therefore, the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

Pair Factors of 60

The pair factors of 60 can be positive or negative, but they cannot be decimal or fraction. The pair factor of 60 is the multiplication of two numbers, resulting in the original number 60. The following are the positive and negative pair factors of 60.

Positive Pair Factors of 60:

Positive Factors of 60	Positive Pair Factors of 60
1 × 60	(1, 60)
2 × 30	(2, 30)
3 × 20	(3, 20)
4 × 15	(4, 15)
5 × 12	(5, 12)
6 × 10	(6,10)

Negative Pair Factors of 60:

Negative Factors of 60	Negative Pair Factors of 60
-1 × -60	(-1, -60)
-2 × -30	(-2, -30)
-3 × -20	(-3, -20)
-4 × -15	(-4, -15)
-5 × -12	(-5, -12)
-6 × -10	(-6, -10)

Prime Factorization of 60

The number 60 is a composite number. Now let us find the prime factors of it.

The first step is to divide the number 60 with the smallest prime factor,i.e. 2.

60 ÷ 2 = 30

Now, check whether 30 can be further divided by 2 or not.

30 ÷ 2 = 15

15 ÷ 2 = 7.5

But, factors cannot be a fraction. Therefore, we will proceed to the next prime number, which is 3.

Now, dividing 15 by 3 we get,

15 ÷ 3 = 5

Again, dividing 5 by 3 will give a fraction number. Therefore, taking the next prime number, 5, into consideration.

5 ÷ 5 = 1

We have received 1 at the end and further, we cannot proceed with the division method, as we know that the multiple of 1 is 1, only. So, the prime factorisation of 60 is 2 × 2 × 3 × 5 or it can be written as 22 × 3 × 5. where 2, 3 and 5 are prime numbers.

Video Lesson on Prime Factors

Get Factors of More Numbers Here

Examples

Example 1:

Find the common factors of 60 and 35.

Solution:

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60

The factors of 35 are 1, 5, 7 and 35.

Therefore, the common factors of 60 and 35 are 1 and 5.

Example 2:

Find the common factors of 60 and 59.

Solution:

Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60

Factors of 59 = 1 and 59

Thus, the common factor of 60 and 59 is 1.

Example 3:

Find the common factors of 60 and 30.

Solution:

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60

The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.

Hence, the common factors of 60 and 30 are 1, 2, 3, 5, 6, 10, 15 and 30.

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The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

The prime factorization of 60 is 2 × 2 × 3 × 5 or 22 × 3 × 5

The positive pair factors of 60 are (1, 60), (2, 30), (3, 20), (4, 15), (5, 12), and (6, 10)

The negative pair factors of 60 are (-1, -60), (-2, -30), (-3, -20), (-4, -15), (-5, -12), and (-6, -10).

No, 35 is not a factor of 60. If 60 is divided by 35, it leaves the remainder, and hence 35 is not a factor of 60.

Here we have a collection of all the information you may need about the Prime Factors of 60. We will give you the definition of Prime Factors of 60, show you how to find the Prime Factors of 60 (Prime Factorization of 60) by creating a Prime Factor Tree of 60, tell you how many Prime Factors of 60 there are, and we will show you the Product of Prime Factors of 60.

Prime Factors of 60 definition

First note that prime numbers are all positive integers that can only be evenly divided by 1 and itself. Prime Factors of 60 are all the prime numbers that when multiplied together equal 60.
How to find the Prime Factors of 60 The process of finding the Prime Factors of 60 is called Prime Factorization of 60. To get the Prime Factors of 60, you divide 60 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 60. See illustration below.

All the prime numbers that are used to divide in the Prime Factor Tree are the Prime Factors of 60. Here is the math to illustrate: 60 ÷ 2 = 3030 ÷ 2 = 1515 ÷ 3 = 55 ÷ 5 = 1 Again, all the prime numbers you used to divide above are the Prime Factors of 60. Thus, the Prime Factors of 60 are: 2, 2, 3, 5.
How many Prime Factors of 60? When we count the number of prime numbers above, we find that 60 has a total of 4 Prime Factors.

Product of Prime Factors of 60

The Prime Factors of 60 are unique to 60. When you multiply all the Prime Factors of 60 together it will result in 60. This is called the Product of Prime Factors of 60. The Product of Prime Factors of 60 is: 2 × 2 × 3 × 5 = 60

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Prime Factors of 61

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