Do you know that ‘factor’ is a Latin word which means ‘a performer’, ‘a doer’ or ‘a maker’?! In mathematics, we use the method of multiplication or division to find the factor of any number. Factoring is an essential and helpful skill to find factors of numbers in mathematics and perform quick calculations in real-life situations. In this article, we will learn everything about the factors of 36 and solve a few example questions to understand the topic better.
We would advise our students to hire a private or online math tutor, clear their doubts and master their factoring skills. Going for extra help after school not only helps students score better or enhance knowledge but also boost confidence in their mental arithmetic skills.
Let us discover and learn everything about the factors of 36.
In mathematics, factors are algebraic expressions that divide other expressions evenly. By definition, a factor is a number that divides the actual or given number with zero remainder. A number has either a positive or a negative factor.
Just like multiplication tables, addition and subtraction, factors are also a part of our daily life. Whether you have to pay bills, handle money, solve ratios, arrange data or compare prices, the knowledge of factors is required.
Multiplying two or more numbers produces the factors of a certain number. For instance, to find the factors of 6, we will determine its multiples such as,
⇒ 1 x 6 = 6
also
⇒ 2 x 3 = 6
Thus 1, 2, 3 and 6 are the factors of 6.
Numbers or integers which divide 36 with zero remainders are called the factors of 36. They are multiplied in pairs to generate the natural number 36, and it could be positive or negative numbers. Multiplying the pair of negative numbers results in the positive original number. 36 is the composite number and the biggest factor among 9 factors of 36. Thus, the nine factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Factors of 36
| Factors | 1, 2, 3, 4, 6, 9, 12, 18, 36 |
| Positive Factors | 2, 3 |
| Negative Factors | -1, -2, -3, -4, -6, -9, -12, -18, -36 |
| Prime Factorization | 22, 32 |
| Sum of Factors | 91 |
There are numerous ways to find the factors of 36, such as divisibility rules, upside-down division method and prime factorization. However, the easiest way to find factors of 36 is by finding two numbers whose product result is 36. Let us take an example to determine the factors of 36.
Divide 36 by a number that leaves 0 remainder such as 2.
⇒ 36/2 = 18
Here,
⇒ 18 = Quotient
⇒ 2 = Divisor
⇒ 0 = Remainder
Since 18 x 2 = 36, thus 18 and 2 are the factors of 36.
Here (2, 18) are the pair factors of 36
Pair factors are the set of 2 multipliers whose product result generates the original number that is 36. Pair factors come in both ways; negative and positive.
Go through the table given below to learn all positive and negative factors and pair factors of 36:
Factors of 36
| Positive Factors | Positive Pair Factors | Negative Factors | Negative Pair Factors |
| 1 x 36 | (1, 36) | -1 x -36 | (-1, -36) |
| 2 x 18 | (2, 18) | -2 x -18 | (-2, -18) |
| 3 x 12 | (3, 12) | -3 x -12 | (-3, -12) |
| 4 x 9 | (4, 9) | -4 x -9 | (-4, -9) |
| 6 x 6 | (6, 6) | -6 x -6 | (-6, -6) |
A way to express a number as a product of its prime factors is known as prime factorization. Prime factors usually have two factors. In other words, finding a pair of pair numbers that multiply together to generate the original number is called prime factorization.
To calculate the prime factors of any number, divide the actual number with the least prime number and continue the process till the end product is 1.
The process of finding the prime factors of 36 is the same as mentioned above. We will start by dividing 36 with the least prime number, which is 2 and then continues the process till it is completely divisible. Go through the steps given below to learn how to find the prime factorization of 36:
⇒ 36/2 = 18
⇒ 18/2 = 9
⇒ 9/3 = 3
⇒ 3/3 = 1
Here, the prime factors are 2 x 2 x 3 x 3 i.e., 22 x 32
Solution:
Factors of 72 = 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, 72
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Common Factors = 1, 2, 3, 4, 9, 18, 36
Hence, the common factors of 72 and 36 are 1, 2, 3, 4, 9, 18, and 36.
Solution:
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
The sum of these all factors is calculated as
⇒ 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36 = 91
Average sum is calculated as
⇒ 91/9 = 10.11
Solution:
Collect two numbers which generate 36 when multiplied together. Use multiplication tables to find them:
⇒ 1 x 36 = 36
⇒ 4 x 9 = 36
⇒ 6 x 6 = 36
⇒ 12 x 3 = 36
⇒ 18 x 2 = 36
Now club the numbers in pairs in the following manner
= (1, 36), (4, 9), (6, 6), (12, 3), (18, 2)
Hence the 5-factor pairs of 36 are (1, 36), (4, 9), (6, 6), (12, 3), and (18, 2).
Solution:
Prime Factors of 36 = 2 x 3
Product of Prime Factors = 6
Solution:
Factors of 63 = 1, 3, 7, 9, 21
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Common Factors of 63 and 36 = 1, 3, 9
Greatest Common Factor (GCF) of 63 and 36 = 9
An algebraic expression or a number that evenly divides a number with no remainder. In other words, multipliers are the factors of product results.
Example of factors:
Factor of 9 = 1, 3, 9
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 37 = 1, 37
Following are the three positive and negative pairs of 36:
Positive Pairs = (1, 36), (2, 18), and (3, 12)
Negative Pairs = (-1, -36), (-2, -18), and (-3, -12)
No, 21 is not a factor of 36. As 36 is not completely divisible by 21, that is why it is not the factor of 36.
36 has a total nine (9) factor, which shows 36 is completely divisible by nine natural numbers such as 1, 2, 3, 6, 9, 12, 18 and 36.
