# Factors 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

#### How to find factors of a number

 1.   Find factors of 300 using Division Method 2.   Find factors of 300 using Prime Factorization 3.   Find factors of 300 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 300

• Divide 300 by 1: 300 ÷ 1 : Remainder = 0
• Divide 300 by 2: 300 ÷ 2 : Remainder = 0
• Divide 300 by 3: 300 ÷ 3 : Remainder = 0
• Divide 300 by 4: 300 ÷ 4 : Remainder = 0
• Divide 300 by 5: 300 ÷ 5 : Remainder = 0
• Divide 300 by 6: 300 ÷ 6 : Remainder = 0
• Divide 300 by 10: 300 ÷ 10 : Remainder = 0
• Divide 300 by 12: 300 ÷ 12 : Remainder = 0
• Divide 300 by 15: 300 ÷ 15 : Remainder = 0
• Divide 300 by 20: 300 ÷ 20 : Remainder = 0
• Divide 300 by 25: 300 ÷ 25 : Remainder = 0
• Divide 300 by 30: 300 ÷ 30 : Remainder = 0
• Divide 300 by 50: 300 ÷ 50 : Remainder = 0
• Divide 300 by 60: 300 ÷ 60 : Remainder = 0
• Divide 300 by 75: 300 ÷ 75 : Remainder = 0
• Divide 300 by 100: 300 ÷ 100 : Remainder = 0
• Divide 300 by 150: 300 ÷ 150 : Remainder = 0
• Divide 300 by 300: 300 ÷ 300 : Remainder = 0

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

#### 2. Steps to find factors of 300 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 300 using the division method, follow these steps:

• Step 1. Start dividing 300 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 300, which is 2. Divide 300 by 2 to obtain the quotient (150).
300 ÷ 2 = 150
• Step 3. Repeat step 1 with the obtained quotient (150).
150 ÷ 2 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

So, the prime factorization of 300 is, 300 = 2 x 2 x 3 x 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 300 as shown below:

So, the prime factorization of 300 is, 300 = 2 x 2 x 3 x 5 x 5.

#### 3. Find factors of 300 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 300 would be the two numbers which, when multiplied, give 300 as the result.

The following table represents the calculation of factors of 300 in pairs:

Factor Pair Pair Factorization
1 and 300 1 x 300 = 300
2 and 150 2 x 150 = 300
3 and 100 3 x 100 = 300
4 and 75 4 x 75 = 300
5 and 60 5 x 60 = 300
6 and 50 6 x 50 = 300
10 and 30 10 x 30 = 300
12 and 25 12 x 25 = 300
15 and 20 15 x 20 = 300

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 300. They are called negative pair factors.

Hence, the negative pairs of 300 would be ( -1 , -300 ) , ( -2 , -150 ) , ( -3 , -100 ) , ( -4 , -75 ) , ( -5 , -60 ) , ( -6 , -50 ) , ( -10 , -30 ) , ( -12 , -25 ) and ( -15 , -20 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 300 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 300.
• Every number is a factor of zero (0), since 300 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300 are exact divisors of 300.
• Factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300. Each factor divides 300 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300 are all less than or equal to 300.

• What are the prime 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, 300.
Prime factors of 300 are 2, 2, 3, 5, 5.

• What two numbers make 300?

Two numbers that make 300 are 2 and 150.

• What is the greatest prime factors of 300?

The greatest prime factor of 300 is 5.

• What are factors of 300?

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

• How do you find factors of a negative number? ( eg. -300 )?

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

• What are five multiples of 300?

First five multiples of 300 are 600, 900, 1200, 1500, 1800.

• Write some multiples of 300?

First five multiples of 300 are 600, 900, 1200, 1500.

• Is 300 a perfect square?

No 300 is not a perfect square.

• What two numbers make 300?

Two numbers that make 300 are 2 and 150.

#### Examples of Factors

What is prime factorization of 300?

Prime factorization of 300 is 2 x 2 x 3 x 5 x 5 = 22 x 3 x 52.

Sammy is puzzled while calculating the prime factors of 300. Can you help him find them?

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

Kevin has been asked to write 17 factor(s) of 300. Can you predict the answer?

17 factor(s) of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150.

Joey wants to write all the prime factors of 300 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 300 are 2, 2, 3, 5, 5.
So in exponential form it can be written as 22 x 3 x 52.

How many factors are there for 300?

Factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300.
So there are in total 18 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 300? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300.
Negative factors are -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -25, -30, -50, -60, -75, -100, -150, -300.

Can you help Rubel to find out the product of the even factors of 300?

Factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300.
Even factors of 300 are 2, 4, 6, 10, 12, 20, 30, 50, 60, 100, 150, 300.
Hence, product of even factors of 300 is; 2 x 4 x 6 x 10 x 12 x 20 x 30 x 50 x 60 x 100 x 150 x 300 = 46656000000000000.