Factor of 36
The factors of 36 are the numbers that divide 36 exactly without leaving the remainder. The factors of 36 can be positive as well as negative, but the factors of 36 cannot be decimal or fraction. For example, the factors of 36 can be (1, 36) or (-1, -36). If we multiply the pair of negative numbers, such as multiplying -1 and -36, it will result in the original number. In this article, we are going to learn the factors of 36, pair factors and the prime factors of 36 and many solved examples.
Table of Contents:
What are the Factors of 36?
The factors of 36 are the numbers, which are multiplied in pairs resulting in the original number 36. As the number 36 is a composite number, it has many factors other than one and the number itself. Thus, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36 Prime Factorization of 36: 2 × 2 × 3 × 3 or 2^{2} × 3^{2} |
Pair Factors of 36
As discussed above, the pair factors of 36 can be positive as well as negative. The pair factors of 36 are the pair of numbers, which are multiplied together resulting in the original number. The positive and negative pair factors are given below:
Positive Pair Factors of 36:
Positive Factors of 36 |
Positive Pair Factors of 36 |
1 × 36 |
(1, 36) |
2 × 18 |
(2, 18) |
3 × 12 |
(3, 12) |
4 × 9 |
(4, 9) |
6 × 6 |
(6, 6) |
Negative Pair Factors of 36:
Negative Factors of 36 |
Negative Pair Factors of 36 |
-1 × -36 |
(-1, -36) |
-2 × -18 |
(-2, -18) |
-3 × -12 |
(-3, -12) |
-4 × -9 |
(-4, -9) |
-6 × -6 |
(-6, -6) |
Prime Factorization of 36
The process of writing the number as a product of prime factors of 36 is called the prime factorization of 36. To calculate the prime factors of 36, divide it with the least prime number which is 2. When it cannot be divided further with two, divide it with the next prime number which is 3 and continue this process till the end product is 1. This is called prime factorization of a number and a step by step format for 36 is given below.
Step 1: Divide 36 with 2
36 ÷ 2 = 18
Step 2: Again divide 18 with 2
18 ÷ 2 = 9
Step 3: Since 9 is no more divisible by 2, move to the next prime number i.e. 3
9 ÷ 3 = 3
Step 4: Finally, divide 3 with 3 to get 1.
3 ÷ 3 = 1
From the above steps, it can be said that the prime factor of 36 will be 2 × 2 × 3 × 3 i.e. 2^{2} × 3^{2}. It should be noted that the above-mentioned method will not only work for 36 but also for all the large numbers.
Examples
Example 1:
Find the common factors of 36 and 35.
Solution:
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The factors of 35 are 1, 5, 7 and 35.
Thus, the common factor of 36 and 35 is 1.
Example 2:
Find the common factors of 36 and 37.
Solution:
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Factors of 37 = 1 and 37.
Hence, the common factor of 36 and 37 is 1, as 37 is a prime number.
Example 3:
Find the common factors of 36 and 72.
Solution:
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and 72.
Therefore, the common factors of 36 and 72 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
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Frequently Asked Questions on Factors of 36
What are the factors of 36?
The factors of 36 are the numbers that divide 36 exactly without leaving any remainder. Thus, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
What is the prime factorization of 36?
The prime factorization of 36 is 2 × 2 × 3 × 3 or 2^{2} × 3^{2}.
What are the positive pair factors of 36?
The positive pair factors of 36 are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6).
Write down the negative pair factors of 36?
The negative pair factors of 36 are (-1, -36), (-2, -18), (-3, -12), (-4, -9), and (-6, -6).
Is 9 a factor of 36?
Yes, 9 is a factor of 36. As the number 9 divides 36 exactly without leaving a remainder, 9 is a factor of 36.