Factors of 300 – Pairs Factors And Prime Factors

Factors of 300

Factors of 300 are defined as the number (both positive and negative), which gets multiplied and results in the result of 300.

Factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.

By multiplying 2 and 6, we get 12, i.e., 2 × 6 = 12. 2 and 6 are factors of 12. Hence, a number may have two or more factors. It follows that the number 300 has two factors.

This article explains the factors of 300, how to find the factors of a number, and how to find the prime factors of 300.

What are the Factors of 300?

The factors of 300 are all integers that can be evenly divided into specific numbers. We know that any number divided by its factor equals one of the other factors. Thus, by dividing 300 by its factor, we get another factor.

We know that a composite number has more than two factors, so 300 is a composite number. It contains other factors besides 1 and 300.

However, these factors are the exact divisors of 300. As an example, when we divide 300 by 25, we get 12 without any remainder.

What are the Factors of -300?

When we multiply two numbers, and we get -300 as a product, those numbers are the factors of -300. 

Here is the explanation:

-1 × 300 = -300 

 1 × 300 = -300

 -2 × 150 = -300

 2 × -150 = -300

 -3 × 100 = -300 

 3 × -100 = -300 

 -4 × 75 = -300 

  4 × -75 = -300

 -5 × 60  = -300

 5 × -60 = -300

 -6 × 50 = -30

 6 × -50 = -300

 -10 × 30 = -300

 10 × -30 = -300

 -12 × 25 = -300

  12 × -25 = -300

 -15 × 20 = -300 

  15 × -20 = -300

We can get -300 by having (-1, 300), (-2, 150), (-3, 100), (-4, 75), (-5, 60), (-6, 50), (-10, 30), (-12, 25), and (-15, 20) as a pair of factors. Similarly, we can also get -300 by having  (1, -300), (2, -150), (3, -100), (4, -75), (5, -60), (6, -50), (10, -30), (12, -25), and (15, -20)as a pair of factors.

How to Calculate the Factors of 300?

You can use the factorization method to determine the factors of 300 by following the steps below:

Step 1:

Write down the number 300 in your notebook.

Step 2:

Multiply two numbers which, when multiplied, give 300. For instance, multiply 2 by 150 to get 300.

Step 3:

We know that 2 is a prime number with only two factors, namely 1 and the number itself. Hence, we cannot factorize it further.

2 = 1 × 2

Step 4:

150 is not a prime number, so let us proceed with finding other factors.

3 × 100 = 300

4 × 75 = 300

5 × 60 = 300

6 × 50 = 300

10 × 30 = 300

12 × 25 = 300

15 × 20 = 300

20 × 15 = 300

There is a repetition of the number combination here. As a result, factorization must cease.

Step 5:

Thus, the unique numbers obtained here are the factors of 300, namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.

In addition, we can find the factors by the division method.

Factors of 300 in Pairs

You can find the pair factors of 300 by multiplying the two numbers in a pair with 46. The numbers are as follows:

Therefore, the positive pair factors of 300 are (1, 300), (2, 150), (3, 100), (4, 75), (5, 60), (6, 50), (10, 30), (12, 25), (15, 20), etc.

As a result, the negative factors connected to the number 300 are (-1, -300), (-2, -150), (-3, -100), (-4, -75), (-5, -60), (-6, -50), (-10, -30), (-12, -25), (-15, -20), etc.

Factors of 300 that add up to 35

Let’s find the factors of 300 that add up to 35.

20 and 15, 20 + 15 = 35

25 and 10, 25 + 10 = 35

30 and 5, 30 + 5 = 35

Similarly, we can write several combinations of factors of 300 that sum to 35.

Prime factors of 300

The prime factors of 300 can be written as follows using prime factorization.

Step 1:

To see how much 300 is, divide it by the smallest prime number, namely 2.

300 ÷ 2 = 150

Since we got a whole number as a result, 2 is a prime factor of 300.

Step 2:

Now we must divide 150 by the prime number.

150 ÷ 2 = 75

Again, 2 is the prime factor.

Step 3:

Take 75 and divide it by 2.

75 ÷ 2 = 37.5

It is impossible for the prime factor to be the fraction. Therefore, we should move on to the next prime number, which is 3.

75 ÷ 3 = 25

In this case, 3 is the prime factor of 300.

Step 4:

Now we need to divide 25 by prime numbers.

25 ÷ 2 = 12.5 (not a factor)

25 ÷ 3 = 8.33 (not a factor)

25 ÷ 5 = 5

5 ÷ 5 = 1

As a result of the division process, we have received 1 and cannot proceed. Thus, the prime factors are written as 2 × 2 × 3 × 5 × 5 or 22 × 3 × 52, where 2, 3, and 5 are prime numbers.

Get Factors of more Numbers Here

Solved Examples

Example1:

Calculate the common factors of 300 and 52.

Solution:

Factors of 50: 1, 2, 5, 10, 25, and 50.

52 factor =  1, 2, 4, 13, 26, and 52.

As a result, 50 and 52 share the common factors of 1 and 2.

Example 2:

Calculate 300 and 9’s common factors.

Solution:

Factors of 300 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.

Factors of 9 = 1, 3, and 9.

Thus, the common factor of 300 and 9 is 1 and 3.

Example 3:

Calculate the common factors of 300 and 24.

Solution:

The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.

All 24 factors= 1, 2, 3, 4, 6, 8, 12, and 24.

Therefore, the common factors of 300 and 24 are 1, 2, 3, 4, 6, and 12.

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