# Factors of 63

Factors of 63 are 1, 3, 7, 9, 21, and 63

#### How to find factors of a number

 1.   Find factors of 63 using Division Method 2.   Find factors of 63 using Prime Factorization 3.   Find factors of 63 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 63

• Divide 63 by 1: 63 ÷ 1 : Remainder = 0
• Divide 63 by 3: 63 ÷ 3 : Remainder = 0
• Divide 63 by 7: 63 ÷ 7 : Remainder = 0
• Divide 63 by 9: 63 ÷ 9 : Remainder = 0
• Divide 63 by 21: 63 ÷ 21 : Remainder = 0
• Divide 63 by 63: 63 ÷ 63 : Remainder = 0

Hence, Factors of 63 are 1, 3, 7, 9, 21, and 63

#### 2. Steps to find factors of 63 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 63 using the division method, follow these steps:

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

So, the prime factorization of 63 is, 63 = 3 x 3 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 63 as shown below:

So, the prime factorization of 63 is, 63 = 3 x 3 x 7.

#### 3. Find factors of 63 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 63 would be the two numbers which, when multiplied, give 63 as the result.

The following table represents the calculation of factors of 63 in pairs:

Factor Pair Pair Factorization
1 and 63 1 x 63 = 63
3 and 21 3 x 21 = 63
7 and 9 7 x 9 = 63

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 63. They are called negative pair factors.

Hence, the negative pairs of 63 would be ( -1 , -63 ) , ( -3 , -21 ) and ( -7 , -9 ) .

#### 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

• Every number is a factor of zero (0), since 63 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, 3, 7, 9, 21, 63 are exact divisors of 63.
• Factors of 63 are 1, 3, 7, 9, 21, 63. Each factor divides 63 without leaving a remainder.

• Which is the smallest prime factor of 63?

Smallest prime factor of 63 is 3.

• Is 63 a perfect square?

No 63 is not a perfect square.

• What are five multiples of 63?

First five multiples of 63 are 126, 189, 252, 315, 378.

• What is prime factorization of 63?

Prime factorization of 63 is 3 x 3 x 7.

• What are factors of 63?

Factors of 63 are 1, 3, 7, 9, 21, 63.

• How do you find factors of a negative number? ( eg. -63 )?

Factors of -63 are -1, -3, -7, -9, -21, -63.

• Is 63 a whole number?

Yes 63 is a whole number.

• Which is greatest factor of 63?

The greatest factor of 63 is 21.

• What are the prime factors of 63?

The factors of 63 are 1, 3, 7, 9, 21, 63.
Prime factors of 63 are 3, 3, 7.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 63. Can you help her?

Prime factors of 63 are 3, 3, 7.
Hence, the product of prime factors of 21.

Can you help Rubel to find out the product of the even factors of 63?

Factors of 63 are 1, 3, 7, 9, 21, 63.
Even factors of 63 are 0.
Hence, product of even factors of 63 is; 0 = 0.

Joy wants to calculate mean of all the factors of 63. Help him in finding the mean of 63.

Factors of 63 are 1, 3, 7, 9, 21, 63.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 63 is 1 + 3 + 7 + 9 + 21 + 63 = 104.
Hence, the mean of factors of 63 is 104 ÷ 6 = 17.33.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 63? Help her in writing all the factors.

Positive factors are 1, 3, 7, 9, 21, 63.
Negative factors are -1, -3, -7, -9, -21, -63.

How many factors are there for 63?

Factors of 63 are 1, 3, 7, 9, 21, 63.
So there are in total 6 factors.

Joey wants to write all the prime factors of 63 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 63 are 3, 3, 7.
So in exponential form it can be written as 32 x 7.

Kevin has been asked to write 5 factor(s) of 63. Can you predict the answer?

5 factor(s) of 63 are 1, 3, 7, 9, 21.