Factors of 36 – Prime Factorization, Factor Pairs, and Examples

Updated: August 14, 2025

|

Category: Advance Math, Math

The factors of 36 are numbers that divide 36 exactly without leaving a remainder. In other words, if you multiply two whole numbers together and the result is 36, both of those numbers are factors of 36.

Understanding factors is an important math skill, especially for simplifying fractions, finding greatest common factors, and solving multiplication or division problems. Let’s explore the factors of 36, its prime factorization, factor pairs, and more.

Definition of Factors

A factor is a number that divides another number evenly. For example, since 6 × 6 = 36, the number 6 is a factor of 36. Similarly, 4 × 9 = 36, so 4 and 9 are also factors of 36.

All Factors of 36

To find all factors of 36, we check which numbers from 1 to 36 divide it evenly:

Factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36

Factor Pairs of 36

Factors often come in pairs because two numbers multiplied together give the original number.

Factor pairs of 36:

1 × 36
2 × 18
3 × 12
4 × 9
6 × 6

Prime Factors of 36

Prime factors are the prime numbers that multiply together to make a given number.

Step-by-step Prime Factorization of 36:

36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1 (stop here)

So, the prime factors of 36 are:
2 × 2 × 3 × 3 or 2² × 3²

Is 36 a Perfect Square?

Yes. 36 is a perfect square because it can be expressed as 6 × 6.

Real-Life Examples of the Number 36

A standard roulette wheel has 36 numbers.
In some sports, scoring systems include 36 as a milestone.
Certain board games have 36 squares or spots.

Fun Facts About the Number 36

36 is a triangular number (sum of the first 8 natural numbers).
In Roman numerals, 36 is written as XXXVI.
It’s a highly composite number with more factors than most smaller numbers.

Conclusion

The factors of 36 include a mix of small and large numbers, making it a perfect example for learning about factors, multiples, and prime factorization. Whether you’re simplifying fractions or solving math puzzles, understanding how to find and use factors is an essential skill. With 1, 2, 3, 4, 6, 9, 12, 18, and 36 as its factors, the number 36 is both versatile and mathematically interesting.

Want to spark your child’s interest in math and boost their skills? Moonpreneur’s online math curriculum stands out because it engages kids with hands-on lessons, helps them apply math in real-life situations, and makes learning math exciting!

You can opt for our Advanced Math or Vedic Math+Mental Math courses. Our Math Quiz for grades 3rd, 4th, 5th, and 6th helps in further exciting and engaging in mathematics with hands-on lessons.

Related Blogs:

$Moonpreneur$

Moonpreneur

Moonpreneur is an ed-tech company that imparts tech entrepreneurship to children aged 6 to 15. Its flagship offering, the Innovator Program, offers students a holistic learning experience that blends Technical Skills, Power Skills, and Entrepreneurial Skills with streams such as Robotics, Game Development, App Development, Advanced Math, Scratch Coding, and Book Writing & Publishing.