The factors of 240 are the numbers that divide 240 exactly without leaving any remainder. The factors and the pair factors of 240 can be expressed in positive or negative forms. For example, the pair factor of 240 can be written as (1, 240) or (-1, -240). If we multiply a pair of negative numbers, such as multiplying -1 and -240 results in the original number. In this article, we will learn what are the factors of 240, pair factors and the prime factors of 240 using the prime factorization and many solved examples.
Table of Contents:
- What are the Factors of 240?
- Pair Factors of 240
- Factors of 240 by Division Method
- Prime Factorization of 240
- Solved Examples
- FAQs
What are the Factors of 240?
The numbers that divide 240 completely and leave a remainder 0 are the factors of 240. In other words, the factors of 240 are the numbers that are multiplied in pairs resulting in the original number 240. As 240 is an even composite number, it has more than two factors. Thus, 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. Similarly, the negative 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.
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 Ã— 2 Ã— 2 Ã— 2 Ã— 3 Ã— 5 or 2^{4} Ã— 3 Ã— 5. |
Pair Factors of 240
A pair of numbers that are multiplied together resulting in an original number 240 is called the pair factor of 240. As discussed above, the pair factor of 240 is expressed in positive and negative form. The number 240 has many factor pairs, as it is an even composite number. The following are the positive and negative pair factors of 240.
Positive pair Factors of 240:
Positive Factors of 240 |
Positive Pair Factors of 240 |
1 Ã— 240 |
(1, 240) |
2 Ã— 120 |
(2, 120) |
3 Ã— 80 |
(3, 80) |
4 Ã— 60 |
(4, 60) |
5 Ã— 48 |
(5, 48) |
6 Ã— 40 |
(6, 40) |
8 Ã— 30 |
(8, 30) |
10 Ã— 24 |
(10, 24) |
12 Ã— 20 |
(12, 20) |
15 Ã— 16 |
(15, 16) |
Therefore, the positive pair factors of 240 are (1, 240), (2, 120), (3, 80), (4, 60) ,(5, 48), (6, 40), (8, 30), (10, 24), (12, 20) and (15, 16).
Negative Pair Factors of 240:
Negative Factors of 240 |
Negative Pair Factors of 240 |
-1 Ã— -240 |
(-1, -240) |
-2 Ã— -120 |
(-2, -120) |
-3 Ã— -80 |
(-3, -80) |
-4 Ã— -60 |
(-4, -60) |
-5 Ã— -48 |
(-5, -48) |
-6 Ã— -40 |
(-6, -40) |
-8 Ã— -30 |
(-8, -30) |
-10 Ã— -24 |
(-10, -24) |
-12 Ã— -20 |
(-12, -20) |
-15 Ã— -16 |
(-15, -16) |
Therefore, the negative pair factors of 240 are (-1, -240), (-2, -120), (-3, -80), (-4, -60) ,(-5, -48), (-6, -40), (-8, -30), (-10, -24), (-12, -20) and (-15, -16).
Factors of 240 by Division Method
In the division method, the number 240 is divisible by different integers. If the integer divides 240 exactly without leaving a remainder, then the integers are the factors of 240. Now, let’s discuss how to find the factors of 240 using the division method.
- 240/1 = 240 (Factor = 1 and Remainder = 0)
- 240/2 = 120 (Factor = 2 and Remainder = 0)
- 240/3 = 80 (Factor = 3 and Remainder = 0)
- 240/4 = 60 (Factor = 4 and Remainder = 0)
- 240/5 = 48 (Factor = 5 and Remainder = 0)
- 240/6 = 40 (Factor = 6 and Remainder = 0)
- 240/8 = 30 (Factor = 8 and Remainder = 0)
- 240/10 = 24 (Factor = 10 and Remainder = 0)
- 240/12 = 20 (Factor = 12 and Remainder = 0)
- 240/15 = 16 (Factor = 15 and Remainder = 0)
- 240/16 = 15 (Factor = 16 and Remainder = 0)
- 240/20 = 12 (Factor = 20 and Remainder = 0)
- 240/24 = 10 (Factor = 24 and Remainder = 0)
- 240/30 = 8 (Factor = 30 and Remainder = 0)
- 240/40 = 6 (Factor = 40 and Remainder = 0)
- 240/48 = 5 (Factor = 48 and Remainder = 0)
- 240/60 = 4 (Factor = 60 and Remainder = 0)
- 240/80 = 3 (Factor = 80 and Remainder = 0)
- 240/120 = 2 (Factor = 120 and Remainder = 0)
- 240/240 = 1 (Factor = 240 and Remainder = 0)
If we divide 240 by any numbers other than 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240, it leaves a remainder value. 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.
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Prime Factorization of 240
The numbers expressed in the form of its prime factors are called the prime factorization method. Now, let us discuss how to find the prime factors of 240 using the prime factorization method.
First, take the pair factor of 240, say (1, 240)
Here, the number 1 cannot be factored further, as 1 is neither prime nor composite.
Now, take the other number 240, which is a composite number. Now, write the two numbers which give the product as 240.
Thus, 240 is written as 15 Ã— 16.
Now, both the numbers 15 and 16 are composite numbers, which can be factored further.
Here, 15 can be expressed as 3 Ã— 5 and 16 can be expressed as 2 Ã— 2 Ã— 2 Ã— 2.
Now, write all the numbers in the form of the product of its prime factors.
Therefore, the prime factorization of 240 is 2 Ã— 2 Ã— 2 Ã— 2 Ã— 3 Ã— 5 or 2^{4} Ã— 3 Ã— 5.
Video Lesson on Prime Factors
Solved Examples
Example 1:
What are the common factors of 240 and 120?
Solution:
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 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.
Hence, the common factors of 240 and 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.
Example 2:
Find the common factors of 240 and 239.
Solution:
Factors of 240 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240.
Factors of 239 = 1 and 239.
As the number 239 is a prime number, the common factor of 240 and 239 is 1.
Example 3:
Find the common factors of 240 and 241.
Solution:
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 241 are 1 and 241.
Therefore, the common factor of 240 and 241 is 1.
Frequently Asked Questions on Factors of 240
What are the factors of 240?
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.
What is the prime factorization of 240?
The prime factorization of 240 is 2 Ã— 2 Ã— 2 Ã— 2 Ã— 3 Ã— 5 or 2^{4} Ã— 3 Ã— 5
What are the positive pair factors of 240?
The positive pair factors of 240 are (1, 240), (2, 120), (3, 80), (4, 60) ,(5, 48), (6, 40), (8, 30), (10, 24), (12, 20) and (15, 16).
What are the negative pair factors of 240?
The negative pair factors of 240 are (-1, -240), (-2, -120), (-3, -80), (-4, -60) ,(-5, -48), (-6, -40), (-8, -30), (-10, -24), (-12, -20) and (-15, -16).
Is 60 a factor of 240?
Yes, 60 is a factor of 240. As 60 divides 240 exactly and leaves a remainder 0, the number 60 is a factor of 240.