# Factors of 378

Factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, and 378

#### How to find factors of a number

 1.   Find factors of 378 using Division Method 2.   Find factors of 378 using Prime Factorization 3.   Find factors of 378 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 378

• Divide 378 by 1: 378 ÷ 1 : Remainder = 0
• Divide 378 by 2: 378 ÷ 2 : Remainder = 0
• Divide 378 by 3: 378 ÷ 3 : Remainder = 0
• Divide 378 by 6: 378 ÷ 6 : Remainder = 0
• Divide 378 by 7: 378 ÷ 7 : Remainder = 0
• Divide 378 by 9: 378 ÷ 9 : Remainder = 0
• Divide 378 by 14: 378 ÷ 14 : Remainder = 0
• Divide 378 by 18: 378 ÷ 18 : Remainder = 0
• Divide 378 by 21: 378 ÷ 21 : Remainder = 0
• Divide 378 by 27: 378 ÷ 27 : Remainder = 0
• Divide 378 by 42: 378 ÷ 42 : Remainder = 0
• Divide 378 by 54: 378 ÷ 54 : Remainder = 0
• Divide 378 by 63: 378 ÷ 63 : Remainder = 0
• Divide 378 by 126: 378 ÷ 126 : Remainder = 0
• Divide 378 by 189: 378 ÷ 189 : Remainder = 0
• Divide 378 by 378: 378 ÷ 378 : Remainder = 0

Hence, Factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, and 378

#### 2. Steps to find factors of 378 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 378 using the division method, follow these steps:

• Step 1. Start dividing 378 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 378, which is 2. Divide 378 by 2 to obtain the quotient (189).
378 ÷ 2 = 189
• Step 3. Repeat step 1 with the obtained quotient (189).
189 ÷ 3 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1

So, the prime factorization of 378 is, 378 = 2 x 3 x 3 x 3 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 378 as shown below:

So, the prime factorization of 378 is, 378 = 2 x 3 x 3 x 3 x 7.

#### 3. Find factors of 378 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 378 would be the two numbers which, when multiplied, give 378 as the result.

The following table represents the calculation of factors of 378 in pairs:

Factor Pair Pair Factorization
1 and 378 1 x 378 = 378
2 and 189 2 x 189 = 378
3 and 126 3 x 126 = 378
6 and 63 6 x 63 = 378
7 and 54 7 x 54 = 378
9 and 42 9 x 42 = 378
14 and 27 14 x 27 = 378
18 and 21 18 x 21 = 378

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 378. They are called negative pair factors.

Hence, the negative pairs of 378 would be ( -1 , -378 ) , ( -2 , -189 ) , ( -3 , -126 ) , ( -6 , -63 ) , ( -7 , -54 ) , ( -9 , -42 ) , ( -14 , -27 ) and ( -18 , -21 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 378 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, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378 are exact divisors of 378.
• 1 is a factor of every number. Eg. 1 is a factor of 378.
• Every number is a factor of zero (0), since 378 x 0 = 0.

• Which is the smallest prime factor of 378?

Smallest prime factor of 378 is 2.

• Is 378 a perfect square?

No 378 is not a perfect square.

• What are five multiples of 378?

First five multiples of 378 are 756, 1134, 1512, 1890, 2268.

• What is prime factorization of 378?

Prime factorization of 378 is 2 x 3 x 3 x 3 x 7.

• What are factors of 378?

Factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378.

• How do you find factors of a negative number? ( eg. -378 )?

Factors of -378 are -1, -2, -3, -6, -7, -9, -14, -18, -21, -27, -42, -54, -63, -126, -189, -378.

• Is 378 a whole number?

Yes 378 is a whole number.

• Which is greatest factor of 378?

The greatest factor of 378 is 189.

• What are the prime factors of 378?

The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378.
Prime factors of 378 are 2, 3, 3, 3, 7.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 378. Can you help her?

Prime factors of 378 are 2, 3, 3, 3, 7.
Hence, the product of prime factors of 42.

Can you help Rubel to find out the product of the even factors of 378?

Factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378.
Even factors of 378 are 2, 6, 14, 18, 42, 54, 126, 378.
Hence, product of even factors of 378 is; 2 x 6 x 14 x 18 x 42 x 54 x 126 x 378 = 326653399296.

Joy wants to calculate mean of all the factors of 378. Help him in finding the mean of 378.

Factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 378 is 1 + 2 + 3 + 6 + 7 + 9 + 14 + 18 + 21 + 27 + 42 + 54 + 63 + 126 + 189 + 378 = 960.
Hence, the mean of factors of 378 is 960 ÷ 16 = 60.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 378? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378.
Negative factors are -1, -2, -3, -6, -7, -9, -14, -18, -21, -27, -42, -54, -63, -126, -189, -378.

How many factors are there for 378?

Factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378.
So there are in total 16 factors.

Joey wants to write all the prime factors of 378 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 378 are 2, 3, 3, 3, 7.
So in exponential form it can be written as 2 x 33 x 7.

Kevin has been asked to write 15 factor(s) of 378. Can you predict the answer?

15 factor(s) of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189.