# Factors of 336

Factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, and 336

#### How to find factors of a number

 1.   Find factors of 336 using Division Method 2.   Find factors of 336 using Prime Factorization 3.   Find factors of 336 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 336

• Divide 336 by 1: 336 ÷ 1 : Remainder = 0
• Divide 336 by 2: 336 ÷ 2 : Remainder = 0
• Divide 336 by 3: 336 ÷ 3 : Remainder = 0
• Divide 336 by 4: 336 ÷ 4 : Remainder = 0
• Divide 336 by 6: 336 ÷ 6 : Remainder = 0
• Divide 336 by 7: 336 ÷ 7 : Remainder = 0
• Divide 336 by 8: 336 ÷ 8 : Remainder = 0
• Divide 336 by 12: 336 ÷ 12 : Remainder = 0
• Divide 336 by 14: 336 ÷ 14 : Remainder = 0
• Divide 336 by 16: 336 ÷ 16 : Remainder = 0
• Divide 336 by 21: 336 ÷ 21 : Remainder = 0
• Divide 336 by 24: 336 ÷ 24 : Remainder = 0
• Divide 336 by 28: 336 ÷ 28 : Remainder = 0
• Divide 336 by 42: 336 ÷ 42 : Remainder = 0
• Divide 336 by 48: 336 ÷ 48 : Remainder = 0
• Divide 336 by 56: 336 ÷ 56 : Remainder = 0
• Divide 336 by 84: 336 ÷ 84 : Remainder = 0
• Divide 336 by 112: 336 ÷ 112 : Remainder = 0
• Divide 336 by 168: 336 ÷ 168 : Remainder = 0
• Divide 336 by 336: 336 ÷ 336 : Remainder = 0

Hence, Factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, and 336

#### 2. Steps to find factors of 336 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 336 using the division method, follow these steps:

• Step 1. Start dividing 336 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 336, which is 2. Divide 336 by 2 to obtain the quotient (168).
336 ÷ 2 = 168
• Step 3. Repeat step 1 with the obtained quotient (168).
168 ÷ 2 = 84
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1

So, the prime factorization of 336 is, 336 = 2 x 2 x 2 x 2 x 3 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 336 as shown below:

So, the prime factorization of 336 is, 336 = 2 x 2 x 2 x 2 x 3 x 7.

#### 3. Find factors of 336 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 336 would be the two numbers which, when multiplied, give 336 as the result.

The following table represents the calculation of factors of 336 in pairs:

Factor Pair Pair Factorization
1 and 336 1 x 336 = 336
2 and 168 2 x 168 = 336
3 and 112 3 x 112 = 336
4 and 84 4 x 84 = 336
6 and 56 6 x 56 = 336
7 and 48 7 x 48 = 336
8 and 42 8 x 42 = 336
12 and 28 12 x 28 = 336
14 and 24 14 x 24 = 336
16 and 21 16 x 21 = 336

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 336. They are called negative pair factors.

Hence, the negative pairs of 336 would be ( -1 , -336 ) , ( -2 , -168 ) , ( -3 , -112 ) , ( -4 , -84 ) , ( -6 , -56 ) , ( -7 , -48 ) , ( -8 , -42 ) , ( -12 , -28 ) , ( -14 , -24 ) and ( -16 , -21 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 336 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 336.
• Every number is a factor of zero (0), since 336 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, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336 are exact divisors of 336.
• Factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336. Each factor divides 336 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336 are all less than or equal to 336.

• What are the prime factors of 336?

The factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336.
Prime factors of 336 are 2, 2, 2, 2, 3, 7.

• What two numbers make 336?

Two numbers that make 336 are 2 and 168.

• What is the greatest prime factors of 336?

The greatest prime factor of 336 is 7.

• What are factors of 336?

Factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336.

• How do you find factors of a negative number? ( eg. -336 )?

Factors of -336 are -1, -2, -3, -4, -6, -7, -8, -12, -14, -16, -21, -24, -28, -42, -48, -56, -84, -112, -168, -336.

• What are five multiples of 336?

First five multiples of 336 are 672, 1008, 1344, 1680, 2016.

• Write some multiples of 336?

First five multiples of 336 are 672, 1008, 1344, 1680.

• Is 336 a perfect square?

No 336 is not a perfect square.

• What two numbers make 336?

Two numbers that make 336 are 2 and 168.

#### Examples of Factors

What is prime factorization of 336?

Prime factorization of 336 is 2 x 2 x 2 x 2 x 3 x 7 = 24 x 3 x 7.

Sammy is puzzled while calculating the prime factors of 336. Can you help him find them?

Factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336.
Prime factors of 336 are 2, 2, 2, 2, 3, 7

Kevin has been asked to write 19 factor(s) of 336. Can you predict the answer?

19 factor(s) of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168.

Joey wants to write all the prime factors of 336 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 336 are 2, 2, 2, 2, 3, 7.
So in exponential form it can be written as 24 x 3 x 7.

How many factors are there for 336?

Factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336.
So there are in total 20 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 336? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336.
Negative factors are -1, -2, -3, -4, -6, -7, -8, -12, -14, -16, -21, -24, -28, -42, -48, -56, -84, -112, -168, -336.

Can you help Rubel to find out the product of the even factors of 336?

Factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336.
Even factors of 336 are 2, 4, 6, 8, 12, 14, 16, 24, 28, 42, 48, 56, 84, 112, 168, 336.
Hence, product of even factors of 336 is; 2 x 4 x 6 x 8 x 12 x 14 x 16 x 24 x 28 x 42 x 48 x 56 x 84 x 112 x 168 x 336 = 4.158667366315583e+22.