Factors of 144
What are the factors of 144?
Numbers that divide 144 without leaving any remainder are known as the factors of 144.
For example, 6 is a factor of 144 because when we divide 144 by 6 it gives us a quotient as 24 and the remainder is 0. Here the quotient is also a factor of 144.
So to check if the number is a factor of 144 or not, divide 144 by that number and verify whether the remainder is zero or not.
Factor list of 144
Hence, the factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
Prime factors of 144
The number 144 is a composite number, that is, it has more than two numbers as factors. To find the prime factors, first, we will divide the number 144 by its smallest prime factor, that is, 2.
144 ÷ 2 = 72
Again divide it by 2;
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
Now, divide by next prime number, that is, 3
9 ÷ 3 = 3
3 ÷ 3 = 1
So, the prime factorization of 144 = 2 × 2 × 2 × 2 × 3 × 3 or 2\(^4\) × 3\(^2\).
This means that 2 and 3 are the prime numbers of 144.
Factor pairs of 144
The factor pairs are two factors that when multiplied together give us the result as the original number.
Example: (6, 24) is the factor pair of 144.
The factor pairs can be a positive pair or a negative pair.
Positive factor pairs of 144: When two positive numbers are multiplied the product is positive.
Hence, the positive factor pairs of 144 are (1, 144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16) and (12, 12).
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Rapid Recall
We can remember the factors of 144 with this step diagram:
Solved Factors of 144 Examples
Example 1: Find the common factor of 144 and 200.
Solution:
Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144
Factors of 200 = 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200
Therefore, the common factors of 144 and 200 are 1, 2, 4, and 8.
Example 2: Find the common factors of 144 and 147.
Solution:
Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144
Factors of 147 = 1, 3, 7, 21, 49, and 147
Therefore, the common factors of 144 and 147 are 1 and 3.
Example 3: John has 144 chocolates and Max has 120 chocolates.
Find the greatest common divisor that can divide the number of chocolates that John has and the number of chocolates that Max has completely.
Solution:
To find the greatest common divisor, we will have to first find the common factors of 144 and 120.
Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.
Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
The common factors of 120 and 144 are 1, 2, 3, 4, 8, 12, and 24.
Therefore, the greatest common factor is 24.
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144
So, the least factor of 144 is 1 and the greatest factor is 144 itself.
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
Sum of factors = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 36 + 48 + 72 + 144 = 403
So, the sum of factors of 144 is 403.
Yes, 16 is a factor of 144. Because when the number 16 divides 144, it leaves the quotient as 9 and the remainder as 0.
The prime factorization of 144 is 2 × 2 × 2 × 2 × 3 × 3 or 2\(^4\) × 3\(^2\) .
The positive factor pairs of 144 are (1, 144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16) and (12, 12).