Factors of 36 using Prime Factorization
What are the Factors of 36?
Factors of 36 are those integers that divide 36 without leaving any remainder; in other words, we can say factors of 36 will divide it evenly.
The factors of 36 can be positive as well as negative but they cannot be decimal numbers or fractions. The quotient obtained on dividing 36 by its factor is also a factor of 36.
Factors of 36?
Factors | Pair factors | Prime factors |
|---|---|---|
1, 2, 3, 4, 6, 9, 12, 18, 36 | (1,36), (2,18), (3,12), (4,9) and (6,6) | 36=2 \( \times \) 2 \( \times \) 3 \( \times \) 3 |
For example, 4 is a factor of 36 because on dividing 36 by 4 it leaves no remainder and 9, the quotient in this division, is also a factor of 36.
Factor List for Number 36
Divisor | Is the number a factor of 36 ? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 \( \times \) 36 = 36 |
2 | Yes, 36 is even | 2 \( \times \) 18 = 36 |
3 | Yes, 3 + 6 = 9 is divisible by 3 | 3 \( \times \) 12 = 36 |
4 | No, 36 ÷ 5 = 7 Remainder = 1 | - |
5 | Yes, 36 ÷ 4 = 9 Remainder = 0 | 4 \( \times \) 9 = 36 |
6 | Yes, 36 is even and divisible by 6 | 6 \( \times \) 6 = 36 |
Prime Factors of 36
A factor tree can be used to determine the prime factors of 36 as shown in the figure.
From the factor tree we can see that on prime factorization of 36 the result is; 2 \( \times \) 2 \( \times \) 3 \( \times \) 3 = 2\( ^2 \) \( \times \) 3\( ^2 \).
This means 2 and 3 are the only prime factors of 36.
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Factor Pairs of 36
The factor pair of any number is a set of two integers which when multiplied result in that number. So the two integers are factors of the number. A factor pair can be negative or positive.
[Note: Product of two negative numbers is positive.]
The factor pair of 36 is the set of two factors of 36 which when multiplied give 36 as the product.
Thus the factor pairs of 36 can be obtained from the list of its factors.
Positive factors of 36 | Positive pair factors of 36 |
|---|---|
1 \( \times \) 36 | (1, 36) |
2 \( \times \) 18 | (2, 18) |
3 \( \times \) 12 | (3, 12) |
4 \( \times \) 9 | (4, 9) |
6 \( \times \) 6 | (6, 6) |
Rapid Recall
Solved Examples
Example 1: 36 pancakes are distributed evenly between a group of 9 children. Find out the number of pancakes each child will get.
Solution:
Number of children = 9
Number of pancakes = 36
Since, 9 is a factor of 36, the pancakes can be divided into equal shares without cutting them into smaller pieces.
Dividing 36 by 4;
36 \( \div \) 9 = 4
Hence, each child will get 4 pancakes.
Example 2: What are the common factors of 36 and 18?
Solution:
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36
Factors of 18 are 1, 2, 3, 6, 9, and 18.
So, the common factors of 36 and 18 are 1, 2, 3, 6, 9 and 18.
Example 3: Find out the common factors of 36 and 72.
Solution:
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36,72.
Therefore, the common factors of 36 and 72 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Prime factorization of 36 is 2\( ^2 \) \( \times \) 3\( ^2 \).
So, prime factors of 36 are 2 and 3.
Yes, 36 is a composite number as it has factors other than 1 and itself, that is, 36. In other words the number 36 has more than two factors. Its factors are 2, 3, 4, 6, 9 and 12 other than 1 and 36.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
So, the smallest factor of 36 is 1 and the greatest factor is 36 itself.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
The sum of the all the factors of 36 is
= 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36 = 91
Hence, the sum is 91.
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
So, the number 36 has 9 factors.