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Factors of 240

240 is a highly composite number. Being an even number, it is a multiple of various numbers like 2, 3, 5 and 10, hence it has many factors. We can say, 240 is a refactorable number, because it is divisible by the count of its divisors. In this mini lesson let us learn to calculate all the factors of 240, the factors of 240 in pairs and the prime factorization of 240.

Factors of 240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240
Prime Factorization of 240: 2 × 2 × 2 × 2 × 3 × 5 = 2⁴× 3 × 5

1.	What Are The Factors of 240?
2.	How to Calculate Factors of 240?
3.	Factors of 240 in Pairs
4.	FAQs on Factors of 240

What are the Factors of 240?

The factors of 240 are the numbers that divide 240 without any remainder. The procedure best followed is to use the divisibility test done for 240, starting from the whole number 1. 1 divides every number and 240 is divided by itself. Let us find the other divisors, which form the factors of 240. Let's tabulate them as follows:

Divisibility Test

240 ÷ 2 = 120

240 ÷ 3 =80

240 ÷ 4 = 60

240 ÷ 5 = 48

240 ÷ 6 = 40

240 ÷ 8 = 30

240 ÷ 10 = 24

240 ÷ 12 = 20

240 ÷ 15 = 16

We can stop our divisibility test here, as we have obtained all the divisors. The quotient obtained also are the factors of 240.

How to Calculate the Factors of 240?

We divide 240 following the divisibility rules and test the divisibility of numbers starting from 1 upto 120 (half of 240). Then we check if the divisors and the quotient obtained so, on multiplication yield the product 240. Thus we verify the factors of 240. Observe that in the following operations, 240 ÷ Divisor = Quotient, Remainder = 0.

Divisor	Quotient
1	240
2	120
3	80
4	60
5	48
6	40
8	30
10	24
12	20
15	16

Thus the pairs of divisors and quotients make up the product 240. They are all the factors of 240.

Hence, the factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240.

To understand the concept of finding factors by prime factorization better, let us take a few more examples.

Factors of 360: The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360.
Factors of 40: The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
Factors of 180: The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
Factors of 112: The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.
Factors of 216: The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108 and 216.

Factors of 240 by Prime Factorization

We obtain the prime factors by using prime factorization. Starting from 240, we keep dividing the composite numbers obtained in the process by the smallest factor of that number. Observe the pattern in finding the factors this way shown below. This can be followed using factor tree or upside-division method.

Step 1: 240 ÷ 2 = 120
Step 2: 120 ÷ 2 = 60
Step 3: 60 ÷ 2 = 30
Step 4: 30 ÷ 2 = 15
Step 5: 15 ÷ 3 = 5

This can be followed using factor tree or upside-division method.

finding prime factors using the factor tree of 240

Thus the prime factorization of 240 is 2 × 2 × 2 × 2 × 3 × 5 = 2⁴× 3 × 5.

Important Notes:

There are 20 factors of 240. All the 20 when divide 240 leave no remainder.
The prime factors of 240 are 2, 3 and 5.

Factors of 240 in Pairs

Factors of 240 can also be shown in ordered pairs as shown.The pairs which on multiplication yield the product 240 are the pair factors of 240. Thus, the distinct factor-pairs of 240 are : (1, 240), (2, 120), (3, 80), (4, 60) ,(5, 48), (6, 40 ), (8, 30), (10, 24), (12, 20) and (15, 16)

Tips and Tricks

Do the prime factorization of 240 and obtain it as 2⁴× 3 × 5. Add 1 to each exponent and multiply them. Here we have (4+1) × (1 +1) × (1+1) = 5 × 2 × 2 = 20. This product helps us determine the total number of factors of 240.
Multiply 2 × 2 × 2 × 2 × 3 × 5 in all possible ways to get the 20 composite factors.

Example 1: Sandra decides to travel to her native at 240 miles. She decides to reach the place in 8 hours. How much distance will she cover in an hour?

Solution:

8 hours × _____ miles = 240 miles.
We need to find the missing factor. As, 240 ÷ 8 = 30 miles
Sandra has to cover 30 miles in an hour.
Example 2: Philips finds that 24 pizzas cost $240 and 15 pizzas cost $120. Which is a better deal for him?

Solution:

24 pizzas cost $240.
24 pizzas × cost of each pizza = $240. Expressing this mathematically, 24 x _____ = 240. The missing factor is 10. Thus each pizza costs $10, in this case.

15 pizzas cost $120.
15 pizzas × cost of each pizza = $120. Expressing this mathematically, 15 x _____ = 120. The missing factor is 8. Thus each pizza costs $8, in this case.

Therefore, the better deal is for him is to buy 15 pizzas at $120.

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FAQs on Factors of 240

What are the factors of 240?

The factors of 240 and they are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240.

What factors of 240 sum up to 20?

The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240. Hence, the factors of 240 that sum up to 20 are 8 and 12.

What are the prime factors of 240?

The distinct prime factors of 240 are 2 , 3 and 5.

What are the factors of 240 and 80?

The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240. The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.

What are the odd factors of 240?

The odd factors of 240 are 1, 3, 5 and 15.

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