Factors of 63

Factors of 63 include 1, 3, 7, 9, 21 and 63. The factors of 63 are the numbers that can divide 63 with no remainder left. These factors include both positive and negative integers, as well as 1 and 63.

In this article, we will discuss all the topics related to the factors of 63, including all the factors of 63, both prime factors, and methods to find these factors.

What are Factors?

The factor of a number is any number that divides the given number completely without leaving any remainder.

In the case of 63, all the numbers like 1, 3, 7, 9, 21 and 63 are the factors of 63 because they all divide 63 completely without leaving any remainder.

What are Factors of 63?

The factors of 63 are those numbers that can evenly divide 63 without leaving a remainder. For example, 63 can be divided by 3 with a quotient of 21. Similarly.

• 7 is the factor of 63 as 63 ÷ 7 = 9.
• 9 is the factor of 63 as 63 ÷ 9 = 7.
• 21 is the factor of 63 as 63 ÷ 21 = 3
• 63 is the factor of 63 as 63 ÷ 63 = 1

All Factors of 63

All the 6 factors of 63 are: 1, 3, 7, 9, 21 and 63.

Prime Factors of 63

List of all factors of 63 include both prime and composite numbers. However, we can also express 63 as the product of only prime numbers. The numbers 3 x 3 x 7 that multiply together to give back the number 63, are called the prime factors of 63.

Factors of 63 Calculator

How to Find the Factors of 63?

To find the factors of 63, you can use the hit and try method to check if a certain number completely divides 63 or not, but before that keep the following things in mind:

• The number 1 and the number itself are always the factors of the given number.
• The factors of a number are always less than the given number.

Now that we know that 1 and 63 are the factors of 63, we can start checking numbers starting from 2.

Check for 2: 2 doesn’t completely divide 63, hence, 2 is not a factor of 63.

Check for 3: 3 completely divides 63, hence, 3 is a factor of 63.

• 3 x 21 = 63

Check for 4: 4 does not completely divide 63, hence, 4 is not a factor of 63.

Check for 5: 5 doesn’t completely divide 63, so 5 is not a factor of 63.

Check for 6: 6 doesn’t completely divide 63, hence, 6 is a factor of 63.

Check for 7: 7 completely divides 63, hence, 7 is a factor of 63.

• 7 x 9 = 63

You can keep checking further in the same way but here is a little trick to save you time because checking every number until 63 is not feasible:

By far, these are the factor pairs that we have found out:

• 1 × 63 = 63
• 3 × 21 = 63
• 7 x 9 = 63

The next number after 7 that completely divides 63 is 9 with the following factor pair:

• 9 x 7 = 63

You can see that this factor pair is the exact reverse of the the previous factor pair:

• 7 x 9 = 63

This is exactly the point where you can stop checking for further factors because if we take all the values of these factor pairs, we will get all the factors of 63.

In this case, the factors are: 1, 3, 7, 9, 21 and 63

Prime Factorization of 63

To express 63 as the factor of prime numbers, use prime factorization. Prime factorization is a process of repeated division such that the divisor each time is only a prime number. For 63,

• 63 / 3 = 21
• 21 / 3 = 7
• 7 / 7 = 1

You can see here that in each step, we have only used a prime number for division until we completely divide 63. This can be represented as follows:

Factor Tree of 63

Factor tree is a chart that shows all the prime factors of a number in the form of a tree like diagram, for 63 we can make the factor tree of 63 as follows:

Factor Pairs of 63

The factors when multiplied together, give the original number back. These pairs can include both positive and negative numbers. For example, 9 × 7 = 3 × 21 = 63. Thus, (7, 9) and (3, 21) are factor pair of 63.

Positive Factor Pair of 63

All positive factor pairs of 63 are:

• (1, 63): 1 × 63 = 63
• (3, 21): 3 x 21 = 63
• (7, 9): 7 x 9 = 63

Negative Factor Pairs of 63

All negative factor pairs of 63 are:

• (-1, -63): (-1) × (-63) = 63
• (-3, -21): (-3) x (-21) = 63
• (-7, -9): (-7) x (-9) = 63

Solved Examples on Factors of 63

Example 1: Find the common factors of 63 and 69.

Solution:

• Factors of 63 = 1, 3, 7, 9, 21 and 63
• Factors of 69 = 1, 3, 23 and 69

Common factors = 1 and 3.

Example 2: Is 63 a prime number?

Solution:

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

Since 63 has more than two factors, it is not a prime number.

Example 3: Are factors and multiples of 63 the same?

Solution:

No, the factors of 63 are the numbers smaller than or equal to 63, that completely divide 63 whereas, the multiples are the numbers that come in the table of 63 and are equal to and greater than 63.

Example 4: What is the sum of the factors of 63?

Solution:

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

The sum therefore is 104.

Practice Problems on Factors of 63

Problem 1: What is the greatest prime factor of 63?

Problem 2: What is the GCF of 63 and 140.

Problem 3: What is the product of the factors of 63?

Problem 4: Find the common factors of 63 and 27.

Problem 5: What is the product of the greatest and smallest factor of 63?

Factors of 63 Frequently Asked Questions

List all Factors of 63.

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

How do you Find the Factors of 63?

To find the factors of 63, you can divide 63 by various numbers and check which ones result in whole number quotients without remainders.

What is the Prime Factorization of 63?

The prime factorization of 63 is 3 x 3 x 7.

How many Factors does 63 have?

The total factors of 63 are 6.

What is the Highest Prime Factor of 63?

The prime factors of 63 are 3 x 3 x 7. Thus, the highest prime factor is 7.

What is the Sum of All the Factors of 63?

The sum of all the factors of 63 is 104.

Is 63 a Perfect Square?

No, 63 is not a perfect square because it cannot be expressed as the square of an integer.