Factors of 36 With Examples
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.
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 Thirty Six
As discussed above, the pair factors of Thirty Six 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 Thirty Six |
Positive Pair Factors of Thirty Six |
1 × 36 |
(1, 36) |
2 × 18 |
(2, 18) |
3 × 12 |
(3, 12) |
4 × 9 |
(4, 9) |
6 × 6 |
(6, 6) |
Negative Pair Factors of Thirty Six:
Negative Factors of Thirty Six |
Negative Pair Factors of Thirty Six |
-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 Thirty Six but also for all the large numbers.
Examples
Example 1:
Find the common factors of Thirty Six 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 Thirty Six and 35 is 1.
Example 2:
Find the common factors of Thirty Six and 37.
Solution:
Factors of Thirty Six = 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Factors of 37 = 1 and 37.
Hence, the common factor of Thirty Six and 37 is 1, as 37 is a prime number.
Frequently Asked Questions on Factors of Thirty Six
Q1 What are the factors of Thirty Six?
Ans. The factors of Thirty Six 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.
Q2 What is the prime factorization of 36?
Ans. The prime factorization of 36 is 2 × 2 × 3 × 3 or 2^{2} × 3^{2}.
Q3 What are the positive pair factors of Thirty Six?
Ans. The positive pair factors of Thirty Six are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6).
Q4 Write down the negative pair factors of Thirty Six?
Ans. The negative pair factors of Thirty Six are (-1, -36), (-2, -18), (-3, -12), (-4, -9), and (-6, -6).
Q5 Is 9 a factor of Thirty Six?
Ans. Yes, 9 is a factor of Thirty Six. As the number 9 divides 36 exactly without leaving a remainder, 9 is a factor of Thirty Six.
Category: Maths