Factors Of 60 – With Easy Division and Prime Factorization

ECTI Pakistan - factors of 60

Factors Of 60

Mathematically, factors of 60 are, multiplied together to give the original number. To put it differently, any number that divides 60 completely is a factor of it. Furthermore, since 60 is a composite number, we can also drive its factors. 

Other than 60, other composite numbers such as 24, 12, 18, 12, 48, etc., have more than 2. These are the multiples of 60 that are the extended times of 60, such as 60, 120, 180, 240, 300, 360, 420, 480, 540, etc. 

Using the simple multiplication method, we can determine the factors of a number. By multiplying two numbers, say 60, you get another number. In this case, these two numbers constitute the factors. Here, let us look at the factors for 60 in pairs.

What are the Factors of 60?

In mathematics, a factor of 60 is a pair of numbers multiplied together, resulting in 60. To put it another way, the factors of 60 are the numbers that divide 60 exactly. As a composite number, 60 has more than two factors. 

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

ECTI Pakistan - factors of 60

What are the Factors Of -60?

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

When we multiply two numbers to get the product -60, it comes the following:

-1 x  60 =  -60    &   1 x -60 =  -60

-2 x  30 = -60     &  2 x  -30 = -60

-3 x  20 = -60     &  3 x  -20 = -60

-4 x  15 = -60     &  4 x  -15 = -60

-5 x  12 = -60    &  5 x  -12 = -60

-6 x  10 = -60    &  6 x  -10 = -60

How to Find the Factors of 60?

Here are the steps to find the factors for 60:

Start by writing the number 60 in your notebook.

You can multiply 1 and 60 to get 60, so 1 x 60 = 60.

Consider another number pair that gives 60 when multiplied, such as 2 and 30, i.e. 

2 × 30 = 60.

The prime number 2 has only two factors, i.e. the number itself and 1. This means that we cannot factorize it further.

2 = 1 × 2

As an example, let’s use 3 and 20, i.e. 3 x 20 = 30

We cannot factorize 3 further since it is a prime number.

Similarly, we can write the following factors:

4 × 15 = 60

5 × 12 = 60

6 × 10 = 60

12 × 5 = 60

Each pair of numbers is repeated here.

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

ECTI Pakistan - Factor tree of 60

Pair Factors of 60

They cannot be decimal or fractional, but they can be positive or negative. In other words, 60 is the product of two numbers multiplied together. Here are the positive and negative pair factors of 60.

Positive Pair Factors of 60:

Positive Factors of 60Positive 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 60Negative 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

In mathematics, 60 is a composite number. Here are the prime factors of 60.

  • To divide 60, we need to find the smallest prime factor, 2.

60 ÷ 2 = 30

  • Let’s see if 30 can be divided further by 2.

30 ÷ 2 = 15

15 ÷ 2 = 7.5

          However, factors are not fractions. Next, we will take a look at 3.

  • When we divide 15 by 3, we get:

15 ÷ 3 = 5

  • Divide 5 by 3 again to get a fraction. Next, consider 5.

5 ÷ 5 = 1

  • Since we received 1 at the end, we can’t use the division method, since the multiple of 1 is only one.

 Hence, 60 has the prime factorization 2 x 2 x 3 x 5, or 22 x 3 x 5. The prime factors are 2, 3, and 5.

ECTI Pakistan - Factors of 60 by prime factorization

Examples

Example 1:

Find the common factor between 60 and 35.

Solution:

60 is composed of 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 

35 has the factors 1, 5, 7, and 35.

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

Example 2:

Find out what 60 and 59 have in common.

Solution:

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

The factors of 59 are 1 and 59

Thus, 60 and 59 have a common factor of 1.

Example 3:

Calculate the common factor of 60 and 30.

Solution:

60 is composed of 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 

30 has the factors 1, 2, 3, 5, 6, 10, 15, and 30.

Therefore, 60 and 30 have the following common factors: 1, 2, 3, 5, 6, 10, 15, and 30.

FAQs

How many factors are there in 60?

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

The prime factorization of 60 is?

You can factorize 60 as 2 × 2 × 3 × 5 or 22 × 3 × 5

What are the positive pair factors of 60?

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

Take a look at the negative factors of 60.

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

35 is a factor of 60, right?

In other words, 35 is not a factor of 60. Divide 60 by 35, and you’re left with the remainder. Therefore, 35 cannot be a factor of 60.
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