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Factors of 270

Factors of 270 are the numbers which when multiplied in pairs give the product as 270. These factors can be negative as well. The number 270 is also is an even composite number, which means that it has several factors. In this lesson, we will calculate the factors of 270, prime factors of 270, and factors of 270 in pairs along with solved examples for a better understanding.

Factors of 270: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270.
Prime Factorization of 270: 270 = 2 × 3 × 3 × 3 × 5

1.	What Are the Factors of 270?
2.	How to Calculate the Factors of 270?
3.	Important Notes
4.	Factors of 270 by Prime Factorization
5.	Factors of 270 in Pairs
6.	FAQs on Factors of 270

What Are the Factors of 270?

The integers that divide 270 without leaving a remainder are its factors. The factors of 270 are the numbers that give the product as 270 when they are multiplied. We factor those numbers repeatedly to get all the factors of 270. The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270.

How to Calculate the Factors of 270?

The factors of the number 270 can be calculated as follows:

Write the smallest factor of 270 (except 1). The smallest factor of 270 is 2, 270 ÷ 2 = 135. Thus, 2 and 135 are the factors of 27
Write the next smallest factor of 3, 270 ÷ 3 = 90. Thus, 3 and 90 are the factors of 270.
Now proceed until you reach 135 (half of 270). Thus, we can verify that there are 16 integers that are factors of 270.

Divisibility Test	Division Equation	Factors
270 is divisible by 1	270 ÷ 1 = 270	1 and 270
270 is divisible by 2	270 ÷ 2 = 135	2 and 135
270 is divisible by 3	270 ÷ 3 = 90	3 and 90
270 is divisible by 5	270 ÷ 5 = 54	5 and 54
270 is divisible by 6	270 ÷ 6 = 45	6 and 45
270 is divisible by 9	270 ÷ 9 = 30	9 and 30
270 is divisible by 10	270 ÷ 10 = 27	10 and 27
270 is divisible by 15	270 ÷ 15 = 18	15 and 18

Important Notes

To find the factors of 270, we must divide it by the smallest prime number 2. We should continue until we get the quotient as 1. We can apply the divisibility rules here.
270 is the highest factor and 1 is the smallest factor of 270.
The sum of all the factors of 270 is 720.

Factors of 270 in Pairs

The pair of factors that give 270 when they are multiplied are known as the factor pairs. There are 8 pairs of factors.

Factorization of 270	Factor Pairs
1 × 270 = 270	(1,270)
2 × 135 = 270	(2,135)
3 × 90 = 270	(3,90)
5 × 54 = 270	(5,54)
6 × 45 = 270	(6,45)
9 × 30 = 270	(9,30)
10 × 27 = 270	(10,27)
15 × 18 = 270	(15,18)

Factors of 270 by Prime Factorization

To find the prime factors of a composite number, keep dividing it by the prime numbers one by one, starting from 2.
Continue division using the prime numbers so that they will divide the remaining composite factors exactly, until there are no composite factors left.
We know that 270 is a composite number.
We know that 270 is divisible by 2. Let's split 270 into its 2 factors, that is, 270 = 135 × 2. Now, 135 is broken further into its factors. 135 is broken as 27 × 5 and 27 is broken as 9 × 3, and 9 can be further split as 3 × 3. Since we have all prime numbers, we can stop here.
Therefore, 270 = 2 × 3 × 3 × 3 × 5

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.

Explore factors using illustrations and interactive examples

Factors of 250:The factors of 250 are 1, 2, 5, 10, 25, 50, 125 and 250
Factors of 245:The factors of 245 are 1, 5, 7, 35, 49 and 245
Factors of 256:The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128 and 256.
Factors of 288:The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16,18, 24, 32, 36, 48, 72, 96,144, and 288
Factors of 75:The factors of 75 are 1, 3, 5, 15, 25 and 75
Factors of 70:The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70

Example 1: Andrew finds two sets of bicycle on sale. A 6-gear bicycle can cost $270, and a 15-gear bicycle can cost $540. Which is the better deal for Andrew?

Solution:

Using factors, Andrew compares the price.
Dividing 270 by 6, we know that 45 and 6 are the factors that make 270.
270 ÷ 6 = 45
Dividing 540 by 15, we know that 36 and 15 are the factors that make 540.
540 ÷ 15 = 36
Using this analysis of comparing prices with the help of factors, Andrew finds the 15-gear bicycle is the better deal.
Example 2: At an average speed of 45 miles per hour, how long would Mike take to travel 270 miles?

Solution:

Mike has to travel 270 miles.
His speed is 45 miles per hour.
270 = 45 × _____
Finding the missing factor, we get 45 × 6 = 270
Thus, Mike would take 6 hours to travel 270 miles.

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FAQs on Factors of 270

What are the factors of 270?

The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270.

What is the sum of all the factors of 270?

The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270. The sum of all these factors is 720.

Is 270 a perfect square?

√270 is not a whole number. Thus, 270 is not a perfect square.

What are the factors of 270 that add up to 33?

The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270. The two factors that add up to 33 are 15 and 18.

What are the common factors of 270 and 300?

The common factors of 270 and 300 are 1, 2, 3, 6, 10,

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