The HCF of 144 and 288 is 144.
Understanding the Highest Common Factor (HCF)
The Highest Common Factor (HCF), also commonly referred to as the Greatest Common Divisor (GCD), is the largest positive integer that divides two or more given integers without leaving any remainder. It represents the largest number that is a factor of all the numbers in a set.
Finding the HCF of 144 and 288
To find the HCF of 144 and 288, we first list all the factors (divisors) for each number. A factor is a number that divides another number completely.
Factors of 144:
The numbers that divide 144 evenly are:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
Factors of 288:
The numbers that divide 288 evenly are:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288.
Identifying Common Factors
Next, we identify the factors that appear in both lists. These are the common factors of 144 and 288:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
Determining the Highest Common Factor
From the list of common factors, the highest (largest) number is the HCF. In this case, the largest common factor is 144.
Key Insight into HCF:
When one number is a multiple of another number, the smaller number is always the HCF of the two numbers. Here, 288 is a multiple of 144 (since 288 = 2 × 144). Therefore, 144 divides both itself and 288, making it the highest common factor.
For a deeper dive into the concept of the Greatest Common Divisor, you can explore resources like Wikipedia's article on the Greatest Common Divisor.
