Write 36 as a product of its prime factors.
The Correct Answer and Explanation is:
Prime Factorization of 36:
The number 36 as a product of its prime factors is:
36 = 2 × 2 × 3 × 3
or
36 = 2² × 3²
Explanation:
To express a number as a product of its prime factors means breaking it down into a set of numbers that are all prime and multiply together to give the original number. A prime number is a number greater than 1 that has only two factors: 1 and itself. Examples of prime numbers include 2, 3, 5, 7, 11, and so on.
Let’s go through the process of factoring 36 step by step.
We begin by dividing 36 by the smallest prime number, which is 2.
36 divided by 2 equals 18, so we write:
36 = 2 × 18
Next, we check 18. It is also divisible by 2.
18 divided by 2 equals 9, so we continue:
36 = 2 × 2 × 9
Now we have 9 left. 9 is not divisible by 2, so we move to the next prime number, which is 3.
9 divided by 3 equals 3, so we write:
36 = 2 × 2 × 3 × 3
Now we are left with 3, which is also a prime number. Dividing 3 by 3 gives 1, so the process is complete.
We have successfully expressed 36 as a product of its prime factors: 2 × 2 × 3 × 3
To make it neater, we can use exponents:
2 × 2 = 2²
3 × 3 = 3²
Therefore, 36 = 2² × 3²
Prime factorization is useful in many areas of mathematics such as finding the greatest common divisor, least common multiple, or simplifying fractions. It helps break down numbers into their fundamental building blocks, which is especially helpful in solving problems involving divisibility and number theory.
