# Factors of 84

Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84

#### How to find factors of a number

 1.   Find factors of 84 using Division Method 2.   Find factors of 84 using Prime Factorization 3.   Find factors of 84 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 84

• Divide 84 by 1: 84 ÷ 1 : Remainder = 0
• Divide 84 by 2: 84 ÷ 2 : Remainder = 0
• Divide 84 by 3: 84 ÷ 3 : Remainder = 0
• Divide 84 by 4: 84 ÷ 4 : Remainder = 0
• Divide 84 by 6: 84 ÷ 6 : Remainder = 0
• Divide 84 by 7: 84 ÷ 7 : Remainder = 0
• Divide 84 by 12: 84 ÷ 12 : Remainder = 0
• Divide 84 by 14: 84 ÷ 14 : Remainder = 0
• Divide 84 by 21: 84 ÷ 21 : Remainder = 0
• Divide 84 by 28: 84 ÷ 28 : Remainder = 0
• Divide 84 by 42: 84 ÷ 42 : Remainder = 0
• Divide 84 by 84: 84 ÷ 84 : Remainder = 0

Hence, Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84

#### 2. Steps to find factors of 84 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 84 using the division method, follow these steps:

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

So, the prime factorization of 84 is, 84 = 2 x 2 x 3 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 84 as shown below:

So, the prime factorization of 84 is, 84 = 2 x 2 x 3 x 7.

#### 3. Find factors of 84 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 84 would be the two numbers which, when multiplied, give 84 as the result.

The following table represents the calculation of factors of 84 in pairs:

Factor Pair Pair Factorization
1 and 84 1 x 84 = 84
2 and 42 2 x 42 = 84
3 and 28 3 x 28 = 84
4 and 21 4 x 21 = 84
6 and 14 6 x 14 = 84
7 and 12 7 x 12 = 84

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 84. They are called negative pair factors.

Hence, the negative pairs of 84 would be ( -1 , -84 ) , ( -2 , -42 ) , ( -3 , -28 ) , ( -4 , -21 ) , ( -6 , -14 ) and ( -7 , -12 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

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

• What are the prime factors of 84?

The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Prime factors of 84 are 2, 2, 3, 7.

• What two numbers make 84?

Two numbers that make 84 are 2 and 42.

• What is the greatest prime factors of 84?

The greatest prime factor of 84 is 7.

• What are factors of 84?

Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.

• How do you find factors of a negative number? ( eg. -84 )?

Factors of -84 are -1, -2, -3, -4, -6, -7, -12, -14, -21, -28, -42, -84.

• What are five multiples of 84?

First five multiples of 84 are 168, 252, 336, 420, 504.

• Write some multiples of 84?

First five multiples of 84 are 168, 252, 336, 420.

• Is 84 a perfect square?

No 84 is not a perfect square.

• What two numbers make 84?

Two numbers that make 84 are 2 and 42.

#### Examples of Factors

What is prime factorization of 84?

Prime factorization of 84 is 2 x 2 x 3 x 7 = 22 x 3 x 7.

Sammy is puzzled while calculating the prime factors of 84. Can you help him find them?

Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Prime factors of 84 are 2, 2, 3, 7

Kevin has been asked to write 11 factor(s) of 84. Can you predict the answer?

11 factor(s) of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42.

Joey wants to write all the prime factors of 84 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 84 are 2, 2, 3, 7.
So in exponential form it can be written as 22 x 3 x 7.

How many factors are there for 84?

Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
So there are in total 12 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 84? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Negative factors are -1, -2, -3, -4, -6, -7, -12, -14, -21, -28, -42, -84.

Can you help Rubel to find out the product of the even factors of 84?

Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Even factors of 84 are 2, 4, 6, 12, 14, 28, 42, 84.
Hence, product of even factors of 84 is; 2 x 4 x 6 x 12 x 14 x 28 x 42 x 84 = 796594176.