# Factors of 392

Factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, and 392

#### How to find factors of a number

 1.   Find factors of 392 using Division Method 2.   Find factors of 392 using Prime Factorization 3.   Find factors of 392 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 392

• Divide 392 by 1: 392 ÷ 1 : Remainder = 0
• Divide 392 by 2: 392 ÷ 2 : Remainder = 0
• Divide 392 by 4: 392 ÷ 4 : Remainder = 0
• Divide 392 by 7: 392 ÷ 7 : Remainder = 0
• Divide 392 by 8: 392 ÷ 8 : Remainder = 0
• Divide 392 by 14: 392 ÷ 14 : Remainder = 0
• Divide 392 by 28: 392 ÷ 28 : Remainder = 0
• Divide 392 by 49: 392 ÷ 49 : Remainder = 0
• Divide 392 by 56: 392 ÷ 56 : Remainder = 0
• Divide 392 by 98: 392 ÷ 98 : Remainder = 0
• Divide 392 by 196: 392 ÷ 196 : Remainder = 0
• Divide 392 by 392: 392 ÷ 392 : Remainder = 0

Hence, Factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, and 392

#### 2. Steps to find factors of 392 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 392 using the division method, follow these steps:

• Step 1. Start dividing 392 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 392, which is 2. Divide 392 by 2 to obtain the quotient (196).
392 ÷ 2 = 196
• Step 3. Repeat step 1 with the obtained quotient (196).
196 ÷ 2 = 98
98 ÷ 2 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 392 is, 392 = 2 x 2 x 2 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 392 as shown below:

So, the prime factorization of 392 is, 392 = 2 x 2 x 2 x 7 x 7.

#### 3. Find factors of 392 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 392 would be the two numbers which, when multiplied, give 392 as the result.

The following table represents the calculation of factors of 392 in pairs:

Factor Pair Pair Factorization
1 and 392 1 x 392 = 392
2 and 196 2 x 196 = 392
4 and 98 4 x 98 = 392
7 and 56 7 x 56 = 392
8 and 49 8 x 49 = 392
14 and 28 14 x 28 = 392

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 392. They are called negative pair factors.

Hence, the negative pairs of 392 would be ( -1 , -392 ) , ( -2 , -196 ) , ( -4 , -98 ) , ( -7 , -56 ) , ( -8 , -49 ) and ( -14 , -28 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 392 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 392.
• Every number is a factor of zero (0), since 392 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, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392 are exact divisors of 392.
• Factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392. Each factor divides 392 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392 are all less than or equal to 392.

• What are the pair factors of 392?

Pair factors of 392 are (1,392), (2,196), (4,98), (7,56), (8,49), (14,28).

• What are five multiples of 392?

First five multiples of 392 are 784, 1176, 1568, 1960, 2352.

• What two numbers make 392?

Two numbers that make 392 are 2 and 196.

• What is the sum of all factors of 392?

The sum of all factors of 392 is 855.

• What are factors of -392?

Factors of -392 are -1, -2, -4, -7, -8, -14, -28, -49, -56, -98, -196, -392.

• What are factors of 392?

Factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392.

• Is 392 a perfect square?

No 392 is not a perfect square.

• Which is the smallest prime factor of 392?

Smallest prime factor of 392 is 2.

• Which is greatest factor of 392?

The greatest factor of 392 is 196.

#### Examples of Factors

Can you help Sammy find out the product of the odd factors of 392?

Factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392.
Odd factors of 392 are 1, 7, 49.
Hence product of odd factors of 392 is; 1 x 7 x 49 = 343.

Joey wants to write all the prime factors of 392 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 392 are 2, 2, 2, 7, 7.
So in exponential form it can be written as 23 x 72.

How many factors are there for 392?

Factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 392. Can you predict the answer?

11 factor(s) of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196.

Sammy is puzzled while calculating the prime factors of 392. Can you help him find them?

Factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392.
Prime factors of 392 are 2, 2, 2, 7, 7

What is prime factorization of 392?

Prime factorization of 392 is 2 x 2 x 2 x 7 x 7 = 23 x 72.

Can you help Rubel to find out the product of the even factors of 392?

Factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392.
Even factors of 392 are 2, 4, 8, 14, 28, 56, 98, 196, 392.
Hence, product of even factors of 392 is; 2 x 4 x 8 x 14 x 28 x 56 x 98 x 196 x 392 = 10578455953408.