# Factors of 2430

Factors of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, and 2430

#### How to find factors of a number

 1.   Find factors of 2430 using Division Method 2.   Find factors of 2430 using Prime Factorization 3.   Find factors of 2430 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 2430

• Divide 2430 by 1: 2430 ÷ 1 : Remainder = 0
• Divide 2430 by 2: 2430 ÷ 2 : Remainder = 0
• Divide 2430 by 3: 2430 ÷ 3 : Remainder = 0
• Divide 2430 by 5: 2430 ÷ 5 : Remainder = 0
• Divide 2430 by 6: 2430 ÷ 6 : Remainder = 0
• Divide 2430 by 9: 2430 ÷ 9 : Remainder = 0
• Divide 2430 by 10: 2430 ÷ 10 : Remainder = 0
• Divide 2430 by 15: 2430 ÷ 15 : Remainder = 0
• Divide 2430 by 18: 2430 ÷ 18 : Remainder = 0
• Divide 2430 by 27: 2430 ÷ 27 : Remainder = 0
• Divide 2430 by 30: 2430 ÷ 30 : Remainder = 0
• Divide 2430 by 45: 2430 ÷ 45 : Remainder = 0
• Divide 2430 by 54: 2430 ÷ 54 : Remainder = 0
• Divide 2430 by 81: 2430 ÷ 81 : Remainder = 0
• Divide 2430 by 90: 2430 ÷ 90 : Remainder = 0
• Divide 2430 by 135: 2430 ÷ 135 : Remainder = 0
• Divide 2430 by 162: 2430 ÷ 162 : Remainder = 0
• Divide 2430 by 243: 2430 ÷ 243 : Remainder = 0
• Divide 2430 by 270: 2430 ÷ 270 : Remainder = 0
• Divide 2430 by 405: 2430 ÷ 405 : Remainder = 0
• Divide 2430 by 486: 2430 ÷ 486 : Remainder = 0
• Divide 2430 by 810: 2430 ÷ 810 : Remainder = 0
• Divide 2430 by 1215: 2430 ÷ 1215 : Remainder = 0
• Divide 2430 by 2430: 2430 ÷ 2430 : Remainder = 0

Hence, Factors of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, and 2430

#### 2. Steps to find factors of 2430 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 2430 using the division method, follow these steps:

• Step 1. Start dividing 2430 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 2430, which is 2. Divide 2430 by 2 to obtain the quotient (1215).
2430 ÷ 2 = 1215
• Step 3. Repeat step 1 with the obtained quotient (1215).
1215 ÷ 3 = 405
405 ÷ 3 = 135
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1

So, the prime factorization of 2430 is, 2430 = 2 x 3 x 3 x 3 x 3 x 3 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2430 as shown below:

So, the prime factorization of 2430 is, 2430 = 2 x 3 x 3 x 3 x 3 x 3 x 5.

#### 3. Find factors of 2430 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 2430 would be the two numbers which, when multiplied, give 2430 as the result.

The following table represents the calculation of factors of 2430 in pairs:

Factor Pair Pair Factorization
1 and 2430 1 x 2430 = 2430
2 and 1215 2 x 1215 = 2430
3 and 810 3 x 810 = 2430
5 and 486 5 x 486 = 2430
6 and 405 6 x 405 = 2430
9 and 270 9 x 270 = 2430
10 and 243 10 x 243 = 2430
15 and 162 15 x 162 = 2430
18 and 135 18 x 135 = 2430
27 and 90 27 x 90 = 2430
30 and 81 30 x 81 = 2430
45 and 54 45 x 54 = 2430

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 2430. They are called negative pair factors.

Hence, the negative pairs of 2430 would be ( -1 , -2430 ) , ( -2 , -1215 ) , ( -3 , -810 ) , ( -5 , -486 ) , ( -6 , -405 ) , ( -9 , -270 ) , ( -10 , -243 ) , ( -15 , -162 ) , ( -18 , -135 ) , ( -27 , -90 ) , ( -30 , -81 ) and ( -45 , -54 ) .

#### 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. 2430 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, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, 2430 are exact divisors of 2430.
• 1 is a factor of every number. Eg. 1 is a factor of 2430.
• Every number is a factor of zero (0), since 2430 x 0 = 0.

• Which is the smallest prime factor of 2430?

Smallest prime factor of 2430 is 2.

• Is 2430 a perfect square?

No 2430 is not a perfect square.

• What are five multiples of 2430?

First five multiples of 2430 are 4860, 7290, 9720, 12150, 14580.

• What is prime factorization of 2430?

Prime factorization of 2430 is 2 x 3 x 3 x 3 x 3 x 3 x 5.

• What are factors of 2430?

Factors of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, 2430.

• How do you find factors of a negative number? ( eg. -2430 )?

Factors of -2430 are -1, -2, -3, -5, -6, -9, -10, -15, -18, -27, -30, -45, -54, -81, -90, -135, -162, -243, -270, -405, -486, -810, -1215, -2430.

• Is 2430 a whole number?

Yes 2430 is a whole number.

• Which is greatest factor of 2430?

The greatest factor of 2430 is 1215.

• What are the prime factors of 2430?

The factors of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, 2430.
Prime factors of 2430 are 2, 3, 3, 3, 3, 3, 5.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 2430. Can you help her?

Prime factors of 2430 are 2, 3, 3, 3, 3, 3, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 2430?

Factors of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, 2430.
Even factors of 2430 are 2, 6, 10, 18, 30, 54, 90, 162, 270, 486, 810, 2430.
Hence, product of even factors of 2430 is; 2 x 6 x 10 x 18 x 30 x 54 x 90 x 162 x 270 x 486 x 810 x 2430 = 1.3177032454057537e+22.

Joy wants to calculate mean of all the factors of 2430. Help him in finding the mean of 2430.

Factors of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, 2430.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 2430 is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 27 + 30 + 45 + 54 + 81 + 90 + 135 + 162 + 243 + 270 + 405 + 486 + 810 + 1215 + 2430 = 6552.
Hence, the mean of factors of 2430 is 6552 ÷ 24 = 273.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2430? Help her in writing all the factors.

Positive factors are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, 2430.
Negative factors are -1, -2, -3, -5, -6, -9, -10, -15, -18, -27, -30, -45, -54, -81, -90, -135, -162, -243, -270, -405, -486, -810, -1215, -2430.

How many factors are there for 2430?

Factors of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, 2430.
So there are in total 24 factors.

Joey wants to write all the prime factors of 2430 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2430 are 2, 3, 3, 3, 3, 3, 5.
So in exponential form it can be written as 2 x 35 x 5.

Kevin has been asked to write 23 factor(s) of 2430. Can you predict the answer?

23 factor(s) of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215.