Factors Of 36 (Explained in Details)

Factors of 36

The factors of 36 are the numbers that can be divided into 36 without leaving any remainder. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

For example, if we divide 36 by 2, we get 18. This means that 2 is a factor of 36 because it divides 36 evenly. Similarly, if we divide 36 by 3, we get 12. This means that 3 is also a factor of 36.

Another example would be to consider the factors of 24. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. If we take 2 and 3 as factors of 24, we can multiply them together to get 6, which is also a factor of 24. This is because 2 x 3 = 6, and 6 divides 24 evenly without any remainder.

In summary, the factors of a number are the numbers that can divide the original number without leaving any remainder. We can find the factors of a number by testing all possible numbers up to the square root of the original number. Factors can be used in many different areas of mathematics, including algebra, geometry, and number theory.

Definition of Factorization of 36

All the integers, including positive and negative whole numbers, that can be divided into 36 without any remainder are known as the factors of 36. Dividing 36 by any of its factors will result in another factor of 36

Definition of Factorization

Factorization is the process of finding the factors of a number, which are the numbers that divide it evenly without leaving a remainder. In other words, it is breaking down a number into its prime factors.

For example, the prime factorization of the number 24 is:

First, divide 24 by the smallest prime number, which is 2: 24 ÷ 2 = 12
Next, divide 12 by 2 again: 12 ÷ 2 = 6
Divide 6 by 2: 6 ÷ 2 = 3
Now 3 is a prime number, so the prime factorization of 24 is: 2 x 2 x 2 x 3, or 2³ x 3.
Another example is the prime factorization of the number 60:

Divide 60 by 2: 60 ÷ 2 = 30
Divide 30 by 2: 30 ÷ 2 = 15
Divide 15 by 3: 15 ÷ 3 = 5
Now 5 is a prime number, so the prime factorization of 60 is: 2 x 2 x 3 x 5, or 2² x 3 x 5.

How to find the factors of even number?

To find the factors of an even number, you can follow these steps:

Identify the even number that you want to find the factors of.

Divide the even number by the smallest even factor possible, which is 2. If the even number is not divisible by 2, it is not an even number and you should stop here.

If the even number is divisible by 2, divide it by 2 and write down the quotient. Keep dividing the quotient by 2 until you cannot divide any further. Write down each of the factors of 2 that you use in the division process.

Once you have found all the factors of 2, divide the quotient by the next smallest factor, which is 3. Keep dividing by increasing factors until you cannot divide any further.

Repeat this process until you have divided by all the possible factors up to the square root of the original even number.

The factors of the even number will be all the numbers that you used as divisors in the division process, including the number 1 and the original even number.

For example, let’s find the factors of the even number 48:

The even number is 48.

Divide 48 by 2, which gives 24.

Divide 24 by 2, which gives 12. Divide 12 by 2, which gives 6. Divide 6 by 2, which gives 3. Therefore, the factors of 2 that we used are 2 x 2 x 2.

Divide 3 into 12, which gives 4. Divide 2 into 4, which gives 2. Therefore, the factors of 3 that we used are 3 x 2.

There are no other factors to test since the square root of 48 is 6.

Therefore, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Summary

The factors of 36 are the numbers that can divide 36 without leaving a remainder. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

To find these factors, you can test all possible numbers that are less than or equal to the square root of 36, which is 6. If a number divides 36 without any remainder, it is a factor of 36.

Testing the numbers 2, 3, 4, and 5, we can see that 2, 3, 4, and 6 are factors of 36. Additionally, we know that 1 and 36 are always factors of any number.

Therefore, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.