Factors of 240 Using Prime Factorization
Factors of 240
What are the Factors of 240?
The numbers that divide 240 without leaving any remainder are known as the factors of 240.
For example, 6 is a factor of 240 because when we divide 240 by 6, it gives us 40 as the quotient, and 0 as the remainder. Here, the quotient is also a factor of 240.
So, to check if a number is a factor of 240 or not, divide 240 by that number and check if the remainder is zero or not.
Factor List of 240
The following table shows us how we can obtain the factors of 240 by applying divisibility rules and division facts.
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.
Prime Factorization of 240
The number 240 is a composite number, that is, it has more than two factors.
To find the prime factors of 240, first we will divide 240 by its smallest prime factor, that is, 2.
240 ÷ 2 = 120
Again, divide it by 2:
120 ÷ 2 = 60
Continue to divide the quotients by 2.
60 ÷ 2 = 30
30 ÷ 2 = 15
Now, divide by the next prime number, that is, 3, as 15 is not divisible by 2.
15 ÷ 3 = 5
Now, divide by the next prime number, that is, 5, as 5 is not divisible by 3.
5 ÷ 5 = 1
So, the prime factorization of 240 = 2 × 2 × 2 × 2 × 3 × 5 or \( 2^4\) × 3 × 5.
The factor tree of 240 can be represented as:
This means that 2, 3 and 5 are the prime factors of 240.
Factor Pairs of 240
A factor pair is a set of two factors that, when multiplied together, result in 240.
Example: (5, 48) is the factor pair of 240 as both 5 and 48 are the factors of 240 and 5 \( \times\) 48 = 240.
Hence, 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).
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Rapid Recall
Factors of 240 are:
Solved Factors of 240 Examples
Example 1:
Find the common factors of 240 and 200.
Solution:
The factors of 240 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240
The factors of 200 = 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200
Therefore, the common factors of 240 and 200 are 1, 2, 4, 5, 8, 10, 20 and 40.
Example 2: Find the common factors of 240 and 250.
Solution:
The factors of 240 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240
The factors of 250 = 1, 2, 5, 10, 25, 50, 125 250
Therefore, the common factors of 240 and 250 are 1, 2, 5 and 10.
Example 3: Find the common factors of 233 and 240.
Solution:
The factors of 233 = 1 and 233
The factors of 240 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240
Therefore, the common factor of 233 and 240 is 1.
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.
So, the smallest factor of 240 is 1, and the greatest factor is 240 itself.
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.
Sum of the factors = 1 + 2+ 3 + 4 + 5+ 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 40 + 48 + 60 +80 + 120 + 240 = 744
So, the sum of factors of 240 is 744.
Yes, 30 is a factor of 240 because when 30 divides 240, it results in 8 as the quotient and 0 as the remainder.
The prime factorization of 240 is 2 × 2 × 2 × 2 × 3 × 5 or \( 2^4\) × 3 × 5.
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).