Factors of 63

The factors of 63 are 1, 3, 7, 9, 21 and 63

 

Negative Factors

 

These are negative counterparts of the positive factors.

Negative factors: -1, -3, -7, -9, -21, -63

 

Prime Factors

Prime factors are the prime numbers themselves, when multiplied together, give 63 as the product.

Prime factors: 3, 7

 

Prime Factorization

Prime factorization involves breaking 63 into its prime factors

It is expressed as 3² × 7¹

 

Table listing the factors of 63

 

 

There are different methods to find the factors of 63.

 

Methods to find the factors of 63:

 

• Multiplication Method

 

• Division Method

 

• Prime Factor and Prime Factorization

 

• Factor Tree
   

The multiplication method finds the pair of factors that give 63 as their product.

 

Step-by-step process

 

Step 1: Find the pair of numbers whose product is 63. 

Step 2: The factors are those numbers, when multiplied, give 63.

Step 3: Make a list of numbers whose product will be 63.

 

A list of numbers whose products are 63 is given below:

 

1 × 63 = 63

3 × 21 = 63

7 × 9  =   63
 

The division method finds the numbers that fully divide the given number. 

Step-by-step process:

 

Step 1: Since every number is divisible by 1, 1 will always be a factor.  Example: 63÷1 = 63

Step 2: Move to the next integer. Both divisor and quotient are the factors. 

 

Picture showing the division method:

 

Multiplying prime numbers to get the given number as their product is called prime factors. Prime factorization is breaking down the number into its prime factors.

 

Prime Factors of 63

 

Number 63 has only one prime factor.

 

Prime factors of 63: 3, 7

 

To find the prime factors of 63, divide 63 with the prime numbers 3 and 7.

 

• 63÷3 = 21

 

• 21÷3 = 7

 

• 7÷7 = 1

 

Prime Factorization of 63:

 

Prime Factorization breaks down the prime factors of 63

Expressed as 3² × 7¹
 

 

The prime factorization is visually represented using the factor tree. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.

 

Factor Tree for 63:

 

Factors of 63 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.

 
Positive Factor Pairs: (1,63), (3,21), (7,9)

Negative Factor Pairs:  (-1,-63), (-3,-21), (-7,-9)
 

Whole Number: Numbers starting from zero.

Factors: Numbers that divide the given number, leaving zero as the remainder.

Prime Factors: Prime numbers that multiply together to form the given number.

Prime Factorization: Process of breaking down the prime factors.

GCF: Greatest Common Factor is the largest possible number seen in two or more numbers.