Factors of 36 are the list of integers that we can split evenly into 36. There are overall 9 factors of 36 among which 36 is the biggest factor and its positive factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The Pair Factors of 36 are (1, 36), (2, 18), (3, 12), (4, 9) and (6, 6) and its Prime Factors are 1, 2, 3, 4, 6, 9, 12, 18, 36.

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Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36Negative Factors of 36: -1, -2, -3, -4, -6, -9, -12, -18 and -36Prime Factors of 36: 2, 3Prime Factorization of 36: 2 × 2 × 3 × 3 = 22 × 32Sum of Factors of 36: 91

Let us explore more about factors of 36 and ways to find them.

 1 What Are the Factors of 36? 2 How to Calculate the Factors of 36? 3 Factors of 36 in Pairs 4 Important Notes 5 FAQs on Factors of 36

## What Are the Factors of 36?

Factors of a number are the numbers that divide the given number exactly without any remainder. According to the definition of factors, factors of 36 are those numbers that exactly divide 36 leaving no remainder. In other words, we can say if two numbers are multiplied and the product is 36, then the numbers are factors of 36.Let us do a hit and trial method to find factors of 36.

Divide 36 ÷ 2 = 18Quotient = 18, remainder = 0Now multiply 18 × 2 = 36Hence, 18 and 2 are the factors of 18.

## How to Calculate the Factors of 36?

We can use different methods like the divisibility test, prime factorization, and the upside-down division method to calculate the factors of 36.The most common method we use to find factors is the prime factorization method.

In prime factorization, we express 36 as a product of its prime factors.In the division method, we see which numbers divide 36 exactly without a remainder.

Let us calculate factors of 36 using the following two methods:

Factors of 36 by prime factorization factor tree methodFactors of 36 by upside-down division method

### Prime Factorization of 36 by Upside-Down Division Method

Now as discussed above, in the prime factorization method we show factors of 36 as a product of prime factors of 36. Follow the steps to find the prime factors of 36 by the prime factorization method.

With the help of divisibility rules, find out the smallest factor of the given number. Here, 36 is an even number. So it is clearly divisible by 2. In other words, 2 divides 36 with no remainder. Therefore, 2 is the smallest prime factor of 36.36 ÷ 2 = 18. Now find the prime factors of the obtained quotient. Repeat Step 1 and Step 2 till we get a prime number as the quotient. Here, 18 is the quotient.18 ÷ 2 = 9. Here, 9 is the quotient. Now find the prime factors of the 9.9 ÷ 3 = 3. Here 3 is the prime number. So we can stop the process.Prime factorization of 36 using upside-down division method is 2 × 2 × 3 × 3 = 2² × 3². ### Prime Factorization of 36 by Factor Tree Method

The factor tree method is another visualization method to represent factors of 36. It also helps in determining prime factors of 36. A factor tree is not unique for a given number. Instead of expressing 36 as 2 × 18, we can express 36 as 6 × 6.

Prime factorization of 36 using factor tree method is 2 × 2 × 3 × 3 = 2² × 3². Explore factors using illustrations and interactive examples

## Factors of 36 in Pairs

Factor pairs are the two numbers that, when multiplied, give the number 36. Find all of the factors of the number 36 using the steps below:

Step I: Start with 1 and the number itself.Step II: Count up by ones to see if you can multiply two numbers together to get your target number.Step III: Stop when you can’t get any more numbers in between.Step IV: Connect the factor pairs.

Factor pairs of 36 are given below:

36 = 1 × 3636 = 4 × 936 = 6 × 636 =12 × 336 = 18 × 2

Let us club the numbers in pairs.

The factors of 36 in pairs are (1, 36), (4, 9), (6, 6), (12, 3), and (18, 2).There are a total of 5 pairs of factors of 36.

We can have negative factors also for a given number.

Since the product of two negative numbers is positive <(-) × (-) = +>.The negative pair factors of 36 are (-1, -36), (-4, -9), (-6, -6), (-12, -3), and (-18, -2)There are a total of 5 negative pairs of factors of 36.

Important Notes:

36 is a composite number as it has factors other than 1 and itself.Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.Pair factors of 36 are (1, 36), (4, 9), (6, 6), (12, 3), and (18, 2).1 is a factor of every number.Prime factorization of 36 is 2 × 2 × 3 × 3 = 2² × 3².

Challenging Questions:

Find the factors of 3600 with the help of techniques used in finding factors of 36.Prove that the factor of a number is always less than or equal to the number itself?

## Solved Examples ## FAQs on Factors of 36

### What are the Factors of 36?

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and its negative factors are -1, -2, -3, -4, -6, -9, -12, -18, -36.

### How Many Factors of 36 are also Factors of 22?

Since, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and the factors of 22 are 1, 2, 11, 22.Hence, <1, 2> are the common factors of 36 and 22.

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### What is the Greatest Common Factor of 36 and 20?

The factors of 36 and 20 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 4, 5, 10, 20 respectively.Common factors of 36 and 20 are <1, 2, 4>.Hence, the GCF of 36 and 20 is 4.

### What is the Sum of all the Factors of 36?

Sum of all factors of 36 = (22 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) = 91