# Factors of 1350

Factors of 1350 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, and 1350

#### How to find factors of a number

 1.   Find factors of 1350 using Division Method 2.   Find factors of 1350 using Prime Factorization 3.   Find factors of 1350 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1350

• Divide 1350 by 1: 1350 ÷ 1 : Remainder = 0
• Divide 1350 by 2: 1350 ÷ 2 : Remainder = 0
• Divide 1350 by 3: 1350 ÷ 3 : Remainder = 0
• Divide 1350 by 5: 1350 ÷ 5 : Remainder = 0
• Divide 1350 by 6: 1350 ÷ 6 : Remainder = 0
• Divide 1350 by 9: 1350 ÷ 9 : Remainder = 0
• Divide 1350 by 10: 1350 ÷ 10 : Remainder = 0
• Divide 1350 by 15: 1350 ÷ 15 : Remainder = 0
• Divide 1350 by 18: 1350 ÷ 18 : Remainder = 0
• Divide 1350 by 25: 1350 ÷ 25 : Remainder = 0
• Divide 1350 by 27: 1350 ÷ 27 : Remainder = 0
• Divide 1350 by 30: 1350 ÷ 30 : Remainder = 0
• Divide 1350 by 45: 1350 ÷ 45 : Remainder = 0
• Divide 1350 by 50: 1350 ÷ 50 : Remainder = 0
• Divide 1350 by 54: 1350 ÷ 54 : Remainder = 0
• Divide 1350 by 75: 1350 ÷ 75 : Remainder = 0
• Divide 1350 by 90: 1350 ÷ 90 : Remainder = 0
• Divide 1350 by 135: 1350 ÷ 135 : Remainder = 0
• Divide 1350 by 150: 1350 ÷ 150 : Remainder = 0
• Divide 1350 by 225: 1350 ÷ 225 : Remainder = 0
• Divide 1350 by 270: 1350 ÷ 270 : Remainder = 0
• Divide 1350 by 450: 1350 ÷ 450 : Remainder = 0
• Divide 1350 by 675: 1350 ÷ 675 : Remainder = 0
• Divide 1350 by 1350: 1350 ÷ 1350 : Remainder = 0

Hence, Factors of 1350 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, and 1350

#### 2. Steps to find factors of 1350 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 1350 using the division method, follow these steps:

• Step 1. Start dividing 1350 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 1350, which is 2. Divide 1350 by 2 to obtain the quotient (675).
1350 ÷ 2 = 675
• Step 3. Repeat step 1 with the obtained quotient (675).
675 ÷ 3 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

So, the prime factorization of 1350 is, 1350 = 2 x 3 x 3 x 3 x 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1350 as shown below:

So, the prime factorization of 1350 is, 1350 = 2 x 3 x 3 x 3 x 5 x 5.

#### 3. Find factors of 1350 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 1350 would be the two numbers which, when multiplied, give 1350 as the result.

The following table represents the calculation of factors of 1350 in pairs:

Factor Pair Pair Factorization
1 and 1350 1 x 1350 = 1350
2 and 675 2 x 675 = 1350
3 and 450 3 x 450 = 1350
5 and 270 5 x 270 = 1350
6 and 225 6 x 225 = 1350
9 and 150 9 x 150 = 1350
10 and 135 10 x 135 = 1350
15 and 90 15 x 90 = 1350
18 and 75 18 x 75 = 1350
25 and 54 25 x 54 = 1350
27 and 50 27 x 50 = 1350
30 and 45 30 x 45 = 1350

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 1350. They are called negative pair factors.

Hence, the negative pairs of 1350 would be ( -1 , -1350 ) , ( -2 , -675 ) , ( -3 , -450 ) , ( -5 , -270 ) , ( -6 , -225 ) , ( -9 , -150 ) , ( -10 , -135 ) , ( -15 , -90 ) , ( -18 , -75 ) , ( -25 , -54 ) , ( -27 , -50 ) and ( -30 , -45 ) .

#### 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. 1350 is a factor of itself.
• 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, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, 1350 are exact divisors of 1350.
• 1 is a factor of every number. Eg. 1 is a factor of 1350.
• Every number is a factor of zero (0), since 1350 x 0 = 0.

• Which is the smallest prime factor of 1350?

Smallest prime factor of 1350 is 2.

• Is 1350 a perfect square?

No 1350 is not a perfect square.

• What are five multiples of 1350?

First five multiples of 1350 are 2700, 4050, 5400, 6750, 8100.

• What is prime factorization of 1350?

Prime factorization of 1350 is 2 x 3 x 3 x 3 x 5 x 5.

• What are factors of 1350?

Factors of 1350 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, 1350.

• How do you find factors of a negative number? ( eg. -1350 )?

Factors of -1350 are -1, -2, -3, -5, -6, -9, -10, -15, -18, -25, -27, -30, -45, -50, -54, -75, -90, -135, -150, -225, -270, -450, -675, -1350.

• Is 1350 a whole number?

Yes 1350 is a whole number.

• Which is greatest factor of 1350?

The greatest factor of 1350 is 675.

• What are the prime factors of 1350?

The factors of 1350 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, 1350.
Prime factors of 1350 are 2, 3, 3, 3, 5, 5.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1350. Can you help her?

Prime factors of 1350 are 2, 3, 3, 3, 5, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 1350?

Factors of 1350 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, 1350.
Even factors of 1350 are 2, 6, 10, 18, 30, 50, 54, 90, 150, 270, 450, 1350.
Hence, product of even factors of 1350 is; 2 x 6 x 10 x 18 x 30 x 50 x 54 x 90 x 150 x 270 x 450 x 1350 = 387420489000000000000.

Joy wants to calculate mean of all the factors of 1350. Help him in finding the mean of 1350.

Factors of 1350 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, 1350.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1350 is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 25 + 27 + 30 + 45 + 50 + 54 + 75 + 90 + 135 + 150 + 225 + 270 + 450 + 675 + 1350 = 3720.
Hence, the mean of factors of 1350 is 3720 ÷ 24 = 155.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1350? Help her in writing all the factors.

Positive factors are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, 1350.
Negative factors are -1, -2, -3, -5, -6, -9, -10, -15, -18, -25, -27, -30, -45, -50, -54, -75, -90, -135, -150, -225, -270, -450, -675, -1350.

How many factors are there for 1350?

Factors of 1350 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, 1350.
So there are in total 24 factors.

Joey wants to write all the prime factors of 1350 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1350 are 2, 3, 3, 3, 5, 5.
So in exponential form it can be written as 2 x 33 x 52.

Kevin has been asked to write 23 factor(s) of 1350. Can you predict the answer?

23 factor(s) of 1350 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675.