What Are Factors Of 36? Definition, Types And Importance - Maths

Factors of 36 - Factorial factors of 36, Prime Factorization method and Fun facts on number 36

Factors of 36 mean the integers that can split 36 into various parts. These integers can be positive and negative. For example, the biggest factor of 36 is 18, and the smallest is 2, excluding 1 and 36.

Factorial facts of 36

• The positive integral pairs of factors of 36 are – (36,1), (2,18), (3,12), (4,9), (6,6).
• Negative pairs of factors of 36 - (-6, -6), (-4, -9), (-3, -12), (-2, -18), (-1, -36)
• Factors of 36 are – 1, 2, 3, 4, 6, 9, 12, 18, 36
• Negative factors of 36 – -1, -2, -3, -4, -6, -9, -12, -18 and -36
• Prime factorization of 36 – 2 x 2 x 3 x 3
• Prime factors of 36 – 2 and 3

Finding factors of 36 using the Prime Factorization method

The prime factorization method is the most common method to represent 36 or any other number. Its other form, the prime factor tree method, is a visual method to represent factors of 36. It 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.

We need to divide 36 from the smallest number to the biggest number as shown-

• With the help of divisibility rules, we need to find out the smallest factor of the given number. Here, we have 36, which is an even number. It is divisible by 2. In other words, 2 divides 36 with no remainder. Therefore, 2 is the smallest prime factor of 36.
• 36 ÷ 2 = 18. We need to repeat the steps with other numbers until we get the remainder of 0.
• 18 ÷ 2 = 9. Here, 9 is the quotient. Now, we need to divide it by other numbers and find the prime factors of the 9.
• 9 ÷ 3 = 3. Here 3 is the prime number. We can execute another step to divide 3 by 3. We will get remainder 1. After that, our process is completed, and we get a factor of 36.

Prime factorization of 36 using the prime factorization method is 2 × 2 × 3 × 3 = 2² × 3².

Fun facts about number 36

1. 36 is the square of six and a triangular number, making it a square, triangular number. It is the smallest square, a triangular number other than one, and it is also the only triangular number other than the one whose square root is also a triangular number.

2. This number is the sum of a twin prime pair (17 + 19), the sum of the cubes of the first three positive integers, and the product of the squares of the first three positive integers.

3. 36 is the number of degrees in the interior angle of each tip of a regular pentagram.

4. 36 is the largest numeric base that some computer systems support because it exhausts the numerals 0–9 and the letters A-Z.

5. The sum of the integers from 1 to 36 is 666.