# Factors of 672

Factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, and 672

#### How to find factors of a number

 1.   Find factors of 672 using Division Method 2.   Find factors of 672 using Prime Factorization 3.   Find factors of 672 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 672

• Divide 672 by 1: 672 ÷ 1 : Remainder = 0
• Divide 672 by 2: 672 ÷ 2 : Remainder = 0
• Divide 672 by 3: 672 ÷ 3 : Remainder = 0
• Divide 672 by 4: 672 ÷ 4 : Remainder = 0
• Divide 672 by 6: 672 ÷ 6 : Remainder = 0
• Divide 672 by 7: 672 ÷ 7 : Remainder = 0
• Divide 672 by 8: 672 ÷ 8 : Remainder = 0
• Divide 672 by 12: 672 ÷ 12 : Remainder = 0
• Divide 672 by 14: 672 ÷ 14 : Remainder = 0
• Divide 672 by 16: 672 ÷ 16 : Remainder = 0
• Divide 672 by 21: 672 ÷ 21 : Remainder = 0
• Divide 672 by 24: 672 ÷ 24 : Remainder = 0
• Divide 672 by 28: 672 ÷ 28 : Remainder = 0
• Divide 672 by 32: 672 ÷ 32 : Remainder = 0
• Divide 672 by 42: 672 ÷ 42 : Remainder = 0
• Divide 672 by 48: 672 ÷ 48 : Remainder = 0
• Divide 672 by 56: 672 ÷ 56 : Remainder = 0
• Divide 672 by 84: 672 ÷ 84 : Remainder = 0
• Divide 672 by 96: 672 ÷ 96 : Remainder = 0
• Divide 672 by 112: 672 ÷ 112 : Remainder = 0
• Divide 672 by 168: 672 ÷ 168 : Remainder = 0
• Divide 672 by 224: 672 ÷ 224 : Remainder = 0
• Divide 672 by 336: 672 ÷ 336 : Remainder = 0
• Divide 672 by 672: 672 ÷ 672 : Remainder = 0

Hence, Factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, and 672

#### 2. Steps to find factors of 672 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 672 using the division method, follow these steps:

• Step 1. Start dividing 672 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 672, which is 2. Divide 672 by 2 to obtain the quotient (336).
672 ÷ 2 = 336
• Step 3. Repeat step 1 with the obtained quotient (336).
336 ÷ 2 = 168
168 ÷ 2 = 84
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1

So, the prime factorization of 672 is, 672 = 2 x 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 672 as shown below:

So, the prime factorization of 672 is, 672 = 2 x 2 x 2 x 2 x 2 x 3 x 7.

#### 3. Find factors of 672 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 672 would be the two numbers which, when multiplied, give 672 as the result.

The following table represents the calculation of factors of 672 in pairs:

Factor Pair Pair Factorization
1 and 672 1 x 672 = 672
2 and 336 2 x 336 = 672
3 and 224 3 x 224 = 672
4 and 168 4 x 168 = 672
6 and 112 6 x 112 = 672
7 and 96 7 x 96 = 672
8 and 84 8 x 84 = 672
12 and 56 12 x 56 = 672
14 and 48 14 x 48 = 672
16 and 42 16 x 42 = 672
21 and 32 21 x 32 = 672
24 and 28 24 x 28 = 672

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 672. They are called negative pair factors.

Hence, the negative pairs of 672 would be ( -1 , -672 ) , ( -2 , -336 ) , ( -3 , -224 ) , ( -4 , -168 ) , ( -6 , -112 ) , ( -7 , -96 ) , ( -8 , -84 ) , ( -12 , -56 ) , ( -14 , -48 ) , ( -16 , -42 ) , ( -21 , -32 ) and ( -24 , -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. 672 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 672.
• Every number is a factor of zero (0), since 672 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, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672 are exact divisors of 672.
• Factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672. Each factor divides 672 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, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672 are all less than or equal to 672.

• How do you find factors of a negative number? ( eg. -672 )?

Factors of -672 are -1, -2, -3, -4, -6, -7, -8, -12, -14, -16, -21, -24, -28, -32, -42, -48, -56, -84, -96, -112, -168, -224, -336, -672.

• What is the sum of all factors of 672?

The sum of all factors of 672 is 2016.

• What is prime factorization of 672?

Prime factorization of 672 is 2 x 2 x 2 x 2 x 2 x 3 x 7.

• What are the pair factors of 672?

Pair factors of 672 are (1,672), (2,336), (3,224), (4,168), (6,112), (7,96), (8,84), (12,56), (14,48), (16,42), (21,32), (24,28).

• What are six multiples of 672?

First five multiples of 672 are 1344, 2016, 2688, 3360, 4032, 4704.

• Is 672 a whole number?

Yes 672 is a whole number.

• Which is the smallest prime factor of 672?

Smallest prime factor of 672 is 2.

• What are five multiples of 672?

First five multiples of 672 are 1344, 2016, 2688, 3360, 4032.

• Write all factors of 672?

Factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672.

#### Examples of Factors

Joey wants to write all the prime factors of 672 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 672 are 2, 2, 2, 2, 2, 3, 7.
So in exponential form it can be written as 25 x 3 x 7.

How many factors are there for 672?

Factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672.
So there are in total 24 factors.

Kevin has been asked to write 23 factor(s) of 672. Can you predict the answer?

23 factor(s) of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336.

Sammy is puzzled while calculating the prime factors of 672. Can you help him find them?

Factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672.
Prime factors of 672 are 2, 2, 2, 2, 2, 3, 7

What is prime factorization of 672?

Prime factorization of 672 is 2 x 2 x 2 x 2 x 2 x 3 x 7 = 25 x 3 x 7.

Ariel has been assigned the task to find the product of all the prime factors of 672. Can you help her?

Prime factors of 672 are 2, 2, 2, 2, 2, 3, 7.
Hence, the product of prime factors of 42.

Can you help Rubel to find out the product of the even factors of 672?

Factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672.
Even factors of 672 are 2, 4, 6, 8, 12, 14, 16, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672.
Hence, product of even factors of 672 is; 2 x 4 x 6 x 8 x 12 x 14 x 16 x 24 x 28 x 32 x 42 x 48 x 56 x 84 x 96 x 112 x 168 x 224 x 336 x 672 = 1.9230593474050623e+31.