Highest Common Factor
The highest common factor, also known as the greatest common divisor, is the largest positive integer that divides two or more numbers without leaving a remainder. It is commonly denoted as HCF or GCD.
To find the highest common factor of two numbers, you can use various methods such as prime factorization, division method, or the Euclidean algorithm.
For example, let’s find the highest common factor of 24 and 36 using the prime factorization method:
Find the prime factors of each number:
- 24 = 2 * 2 * 2 * 3 = 2^3 * 3
- 36 = 2 * 2 * 3 * 3 = 2^2 * 3^2
Identify the common prime factors and their lowest powers:
- Common factors: 2^2 * 3
Multiply the common factors to find the highest common factor:
- HCF(24, 36) = 2^2 * 3 = 12
Therefore, the highest common factor of 24 and 36 is 12.
Finding the highest common factor is important in various mathematical operations, simplifying fractions, and solving mathematical problems.
To find the highest common factor (HCF) of 24 and 36 using the division method, follow these steps:
- Start by dividing the larger number (36) by the smaller number (24):
36 ÷ 24 = 1, with a remainder of 12
- Now divide the divisor (24) by the remainder (12):
24 ÷ 12 = 2
- Divide the remainder from the previous step (12) by the new remainder (0):
12 ÷ 0 = undefined
Since the remainder has become zero, the HCF is the divisor from the last non-zero remainder. In this case, the HCF of 24 and 36 using the division method is 12.
Therefore, the highest common factor of 24 and 36 is 12 when using the division method.