# Factors of 390

Factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, and 390

#### How to find factors of a number

 1.   Find factors of 390 using Division Method 2.   Find factors of 390 using Prime Factorization 3.   Find factors of 390 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 390

• Divide 390 by 1: 390 ÷ 1 : Remainder = 0
• Divide 390 by 2: 390 ÷ 2 : Remainder = 0
• Divide 390 by 3: 390 ÷ 3 : Remainder = 0
• Divide 390 by 5: 390 ÷ 5 : Remainder = 0
• Divide 390 by 6: 390 ÷ 6 : Remainder = 0
• Divide 390 by 10: 390 ÷ 10 : Remainder = 0
• Divide 390 by 13: 390 ÷ 13 : Remainder = 0
• Divide 390 by 15: 390 ÷ 15 : Remainder = 0
• Divide 390 by 26: 390 ÷ 26 : Remainder = 0
• Divide 390 by 30: 390 ÷ 30 : Remainder = 0
• Divide 390 by 39: 390 ÷ 39 : Remainder = 0
• Divide 390 by 65: 390 ÷ 65 : Remainder = 0
• Divide 390 by 78: 390 ÷ 78 : Remainder = 0
• Divide 390 by 130: 390 ÷ 130 : Remainder = 0
• Divide 390 by 195: 390 ÷ 195 : Remainder = 0
• Divide 390 by 390: 390 ÷ 390 : Remainder = 0

Hence, Factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, and 390

#### 2. Steps to find factors of 390 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 390 using the division method, follow these steps:

• Step 1. Start dividing 390 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 390, which is 2. Divide 390 by 2 to obtain the quotient (195).
390 ÷ 2 = 195
• Step 3. Repeat step 1 with the obtained quotient (195).
195 ÷ 3 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1

So, the prime factorization of 390 is, 390 = 2 x 3 x 5 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 390 as shown below:

So, the prime factorization of 390 is, 390 = 2 x 3 x 5 x 13.

#### 3. Find factors of 390 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 390 would be the two numbers which, when multiplied, give 390 as the result.

The following table represents the calculation of factors of 390 in pairs:

Factor Pair Pair Factorization
1 and 390 1 x 390 = 390
2 and 195 2 x 195 = 390
3 and 130 3 x 130 = 390
5 and 78 5 x 78 = 390
6 and 65 6 x 65 = 390
10 and 39 10 x 39 = 390
13 and 30 13 x 30 = 390
15 and 26 15 x 26 = 390

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 390. They are called negative pair factors.

Hence, the negative pairs of 390 would be ( -1 , -390 ) , ( -2 , -195 ) , ( -3 , -130 ) , ( -5 , -78 ) , ( -6 , -65 ) , ( -10 , -39 ) , ( -13 , -30 ) and ( -15 , -26 ) .

#### 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. 390 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, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390 are exact divisors of 390.
• 1 is a factor of every number. Eg. 1 is a factor of 390.
• Every number is a factor of zero (0), since 390 x 0 = 0.

• What are the prime factors of 390?

The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390.
Prime factors of 390 are 2, 3, 5, 13.

• What two numbers make 390?

Two numbers that make 390 are 2 and 195.

• What is the greatest prime factors of 390?

The greatest prime factor of 390 is 13.

• What are factors of 390?

Factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390.

• How do you find factors of a negative number? ( eg. -390 )?

Factors of -390 are -1, -2, -3, -5, -6, -10, -13, -15, -26, -30, -39, -65, -78, -130, -195, -390.

• What are five multiples of 390?

First five multiples of 390 are 780, 1170, 1560, 1950, 2340.

• Write some multiples of 390?

First five multiples of 390 are 780, 1170, 1560, 1950.

• Is 390 a perfect square?

No 390 is not a perfect square.

• What two numbers make 390?

Two numbers that make 390 are 2 and 195.

#### Examples of Factors

What is prime factorization of 390?

Prime factorization of 390 is 2 x 3 x 5 x 13 = 2 x 3 x 5 x 13.

Sammy is puzzled while calculating the prime factors of 390. Can you help him find them?

Factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390.
Prime factors of 390 are 2, 3, 5, 13

Kevin has been asked to write 15 factor(s) of 390. Can you predict the answer?

15 factor(s) of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195.

Joey wants to write all the prime factors of 390 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 390 are 2, 3, 5, 13.
So in exponential form it can be written as 2 x 3 x 5 x 13.

How many factors are there for 390?

Factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390.
So there are in total 16 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 390? Help her in writing all the factors.

Positive factors are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390.
Negative factors are -1, -2, -3, -5, -6, -10, -13, -15, -26, -30, -39, -65, -78, -130, -195, -390.

Can you help Rubel to find out the product of the even factors of 390?

Factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390.
Even factors of 390 are 2, 6, 10, 26, 30, 78, 130, 390.
Hence, product of even factors of 390 is; 2 x 6 x 10 x 26 x 30 x 78 x 130 x 390 = 370150560000.