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Factors of 216

An interesting fact about the factors of 216 is that it has seven single-digit numbers as its factors. These include 1, 2, 3, 4, 6, 8, and 9. Let's learn to calculate the factors of 216, prime factors of 216, and factors of 216 in pairs along with solved examples for a better understanding.

Factors of 216: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216
Prime Factorization of 216: 216 = 2 × 2 × 2 × 3 × 3 × 3

1.	What Are the Factors of 216?
2.	How to Calculate the Factors of 216?
3.	Factors of 216 by Prime Factorization
4.	Factors of 216 in Pairs
5.	FAQs on Factors of 216

What Are the Factors of 216?

Factors of a number are the exact divisors of the number leaving the remainder as 0. The factors of 216 are the numbers that exactly divide 216. Let's divide 216 by a few numbers like 2, 3, and 4.

You will observe that the numbers 2, 3, and 4 are the exact divisors of 216. Hence, they are factors of 216. Now, let's divide 216 by 5. 216 divided by 5 gives 43 as the quotient and 1 as the remainder, but it is not entirely divisible by 5. This means that 5 is not an exact divisor of 216 and hence, it is not a factor.

How to Calculate the Factors of 216?

Factors of 216 are the numbers that give the product as 216 when they are multiplied together.

Can you think of all such pairs of numbers? Look below to see some factors of 216.

Hence, the factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108 and 216.

Explore factors using illustrations and interactive examples

Factors of 81 - The factors of 81 are 1, 3, 9, 27, and 81.
Factors of 108 - The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
Factors of 16 - The factors of 16 are 1, 2, 4, 8, and 16.
Factors of 125 - The factors of 125 are 1, 5, 25, and 125.
Factors of 256 - The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, and 256.
Factors of 512 - The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512.

Factors of 216 by Prime Factorization

Prime factorization is a way of expressing a number as the product of its prime factors.

Examples

Follow the steps given below to find the factors of 216 using prime factorization.

Find the smallest prime number that divides 216 exactly.
Write the resultant after dividing 216 by the smallest prime in one column.
Again find the smallest prime that exactly divides the resultant obtained in step 2 and write the resultant.
Repeat step 3 until you reach the number 1.

Did you observe that we ultimately arrive at only one factorization, that is, 216 = 2 × 2 × 2 × 3 × 3 × 3? This is called the prime factorization of 216. Now that we have done the prime factorization of our number, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not?
And as you might have already guessed, for prime numbers, there are no other factors.

Factors of 216 in Pairs

Factor pairs are the pairs of numbers which when multiplied together gives a product that is equal to the original number. Can you observe that all the products of each pair in the figure given below result in 216?

All these pairs form the factor pairs of 216.

Important Notes:

Factors of 216 are the numbers that exactly divide 216.
The prime factorization of 216 is 216 = 2 × 2 × 2 × 3 × 3 × 3.
The number 216 has eight factor pairs.

Example 1: Sally has many balloons and they are numbered 9, 36, 81, 54, 12, and 27. She wants to know which of the numbers on the balloons are the common factors of 81 and 216. Can you help her?

Solution:

Let's see the factors of 81 and 216

Factors of 81: 1, 3, 9, 27, 81

Factors of 216: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216

Hence, the numbers 9 and 27 are the common factors of 81 and 216.
Example 2: Jolly and Jimmy are playing a game using two dices. They make a two-digit number that turns up on the faces of the dice. If the two-digit number turning up is either a factor of 216 or 215, they score a point.

Round 1 Round 2

Jolly 6, 3 3, 4

Jimmy 4, 2 5, 3

The one who finds the most factors in the 2 rounds is the winner. Can you identify who is the winner?

Solution:

Let's see the factors of 216 and 215.

Factors of 216: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216

Factors of 215: 1, 5, 43, and 215.

Now, let's see the numbers formed by Jolly in both the rounds.

In round 1, Jolly got the pair 6 and 3.

The two-digit number she should go with is 36 which is a factor of 216. The number 63 is neither a factor of 215 nor a factor of 216.

In round 2, Jolly got the pair 3 and 4.

The two-digit number she should go with is 43 which is a factor of 215. The number 34 is neither a factor of 215 nor a factor of 216.

Now, let's see the numbers formed by Jimmy in both the rounds.

In round 1, the two-digit number Jimmy should go with is 24 which is a factor of 216. The number 42 is neither a factor of 215 nor a factor of 216.

In round 2, Jimmy got the pair 5 and 3. Neither 53 nor 35 is a factor of 215 or 216.

Thus, we can see that Jolly identified more factors than Jimmy.

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FAQs on Factors of 216

What two numbers give you 216?

Factor pairs of 216 are the pairs of factors which when multiplied together gives a product that is equal to the number 216.
For example, 27 and 8 are two numbers that give the product as 216 ( 27 × 8 = 216 )

What are the factors of 216 and 215?

Factors of 216: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
Factors of 215: 1, 5, 43, and 215.

What is the prime factorization of 216?

The prime factorization of 216 is 2 × 2 × 2 × 3 × 3 × 3.

Is 216 a perfect square?

216 isn't a perfect square as it cannot be obtained as the product of two same integers.

What are the prime factors of 216?

The prime factors of 216 are 2 and 3.

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