Learn How to Find Prime Factors and Factor Pairs of 36 in Detail
Factors are whole numbers that are multiplied together to generate another number. If a × b = c, then a and b are c’s factors.
- A factor is an integer that divides a given whole number exactly with no remainder.
- Every whole number greater than one has at least two factors.
- When a number is divided by one of its factors, the result is another factor. A factor pair is made up of two factors.
- The products of each factor pair equal the number.
Keep in mind that the first factor pair is always 1 and the number itself.
Key Points Regarding Factors
- A factor is a whole number that divides perfectly without a remainder. Eg, 3 is a factor of 36.
- A factor pair is a pair of factors. They produce a certain product when multiplied together. Eg, 2 and 27 have a product of 54, so 2 and 27 are factors of 54 and (2,27) is a factor pair of 54.
- A multiple is a number that appears in a specific times table. For example, 12 is a multiple of 3 because it appears in the 3 times table. 12 is also a multiple of four because it appears in the four times table
- Understanding factors and factor pairs are aided by knowing multiplication and division facts. Knowing divisibility rules can help you find multiples of a given number.
Let’s understand how to factorize a number in detail by taking the example of the number 36.
Factors of 36
The numbers that divide 36 perfectly without leaving a residual are known as 36 factors. The factors of 36 can be both positive and negative, but they cannot be decimals or fractions. The factors of 36, for example, can be (1, 36) or (-1, -36). When we multiply a pair of negative numbers, such as -1 and -36, the outcome is the original number.
What are the Factors of 36?
The factors of 36 are the numbers multiplied in pairs to produce the original number 36. Since the number 36 is a composite number, it contains numerous factors in addition to one and the number itself. As a result, the 36 factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Pair Factors of 36
As previously stated, the pair factors of 36 can be both positive and negative. The pair factors of 36 are the two numbers multiplied together to produce the original number. The positive and negative pair factors are as follows:
Positive Pair Factors of 36:
Therefore, the positive factor pairs of 36 are (1,36), (2,18), (3,12), (4,9) and (6,6).
Negative PaFactors of 36:
-1 × -36
-2 × -18
-3 × -12
-4 × -9
-6 × -6
Therefore, the positive factor pairs of 36 are (-1,-36), (-2,-18), (-3,-12), (-4,-9) and (-6,-6).
Prime Factorization of 36
The prime factorization of 36 refers to the practice of expressing the number as a product of prime factors of 36. Divide 36 by the least prime number, which is 2, to find the prime factors. When it can no longer be divided by two, divide it by the next prime number, 3, and repeat the process until the end product is 1. This is known as prime factorization, and a step-by-step approach for 36 is shown below.
- Divide 36 by 2
36 ÷ 2 = 18
- Again divide the quotient (18) with 2
18 ÷ 2 = 9
- Since the quotient (9) is no more divisible by 2, move to the next prime number i.e. 3
9 ÷ 3 = 3
- Lastly, divide the quotient (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. 22 × 32.