Factors of 300 are the integers that evenly divide the original number. For example, 2 is the factor of 300 since 2 divides 300 evenly; 300/2 = 150. Since 300 is a composite number, it has more than two factors, i.e.,18. Hence, factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300. We can see, among these factors, 2, 3 and 5 are the prime factors of 300. In this article, you will learn the factors of 300, and how to find the factors of a number and prime factors of 300 in detailed steps.
What are the Factors of 300?
Factors for 300 are the numbers that divide 300 into equal parts. These factors are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300. As we know, any number divided by its factor will equal one of the other factors. Thus, when we divide 300 by its factor, it will be equal to another factor.
We know that 300 is a composite number, that means it has more than two factors. Thus, 300 contains other factors apart from 1 and 300.
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Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300 |
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Prime Factorisation of 300 = 2 x 2 x 3 x 5 x 5 = 22 x 3 x 52 |
However, the factors of 300 are the exact divisors of that number. For example, when we divide 300 by 25, we get 12 without leaving any remainder.
How to Find the Factors of 300?
Go through the steps given below to learn how to find the factors of 300 using factorisation method:
Step 1: First, write the number 300 in your notebook.
Step 2: Find the two numbers, which on multiplication gives 300, say 2 and 150, such as 2 × 150 = 300.
Step 3: We know that 2 is a prime number which has only two factors, i.e. 1 and the number itself. So, 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
Here the combination of numbers is repeated. Thus, we have to stop the factorisation.
Step 5: Therefore, the unique numbers which are obtained here are the factors of 300, i.e., 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
We can also find the factors by division method.
Factors Pairs of 300
To find the pair factors of 300, multiply the 2 numbers in a pair to have the original number as 46. Such numbers are as follows:
| Positive pair Factors | Negative pair Factors |
| 1 × 300 = 300; (1, 300) | (-1) × (-300) = 300; (-1, -300) |
| 2 × 150 = 300; (2, 150) | (-2) × (-150) = 300; (2, 150) |
| 3 × 100 = 300; (3, 100) | (-3) × (-100) = 300; (-3, -100) |
| 4 × 75 = 300; (4, 75) | (-4) × (-75) = 300; (-4, -75) |
| 5 × 60 = 300; (5, 60) | (-5) × (-60) = 300; (-5, -60) |
| 6 × 50 = 300; (6, 50) | (-6) × (-50) = 300; (-6, -50) |
| 10 × 30 = 300; (10, 30) | (-10) × (-30) = 300; (-10, -30) |
| 12 × 25 = 300; (12, 25) | (-12) × (-25) = 300; (-12, -25) |
| 15 × 20 = 300; (15, 20) | (-15) × (-20) = 300; (-15, -20) |
Thus, 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.
And the negative factors of 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 us identify 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 the number 300 that add up t0 35.
Prime factors of 300
By prime factorization method, we can write the prime factors of 300 as given below.
Step 1: The first step is to divide the number 300 with the smallest prime number, i.e. 2.
300 ÷ 2 = 150
We got a whole number as a result, so 2 is a prime factor of 300.
Step 2: We have to divide 150 by the prime number.
150 ÷ 2 = 75
Again, 2 is the prime factor.
Step 3: Divide 75 by 2.
75 ÷ 2 = 37.5
Prime factor cannot be the fraction. Hence, proceed with the next prime number, i.e. 3.
75 ÷ 3 = 25
Here, 3 is the prime factor of 300.
Step 4: Now, we have to divide 25 with prime numbers.
25 ÷ 2 = 12.5 (not a factor)
25 ÷ 3 = 8.33 (not a factor)
25 ÷ 5 = 5
5 ÷ 5 = 1
We have received 1 at the end of the division process and so we cannot proceed further. So, the prime factors are written as 2 × 2 × 3 × 5 × 5 or 22 × 3 × 52, where 2, 3 and 5 are the prime numbers.
Video Lesson on Prime Factors
Solved Examples on Factors of 300
Q.1: What is the maximum number that 300 can be divided into equal parts?
Solution: 300 is a composite number that has 18 factors.
The largest factor of 300 is 300 itself.
Hence, we can divide 300 into 300 equal parts such that the value of each part will be equal to 1.
300/1 = 300
Q.2: What is the second highest factor of 300?
Solution: The second highest factor of 300 is 150.
300/150 = 2
Hence, 150 divides 300 into two equal parts.
Related Articles on Factors
| Factors of 100 | Factors of 101 | Factors of 105 |
| Factors of 108 | Factors of 120 | Factors of 144 |
| Factors of 150 | Factors of 215 | Factors of 216 |
Frequently Asked Questions (FAQs) on Factors of 300
What are the factors of 300?
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
What are the multiples of 300?
The multiples of 300 include 300, 600, 900, 1200, 1500, 1800, 2100, 2400, 2700, 3000, etc.
How many prime factors does 300 have?
The number 300 has five prime factors, such as 2, 2, 3, 5, 5.
What are the factors of 340?
The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170 and 340.
How many factors does 300 have?
There are 18 factors for 300 and they are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
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