find the GCF of 24,144,100
To find the greatest common factor (GCF) of 24, 144, and 100, we can start by finding the prime factorization of each number.
Prime factorization of 24: 2^3 * 3
Prime factorization of 144: 2^4 * 3^2
Prime factorization of 100: 2^2 * 5^2
Now, we can identify the common prime factors and their lowest exponent:
Common prime factors: 2^2 = 4
The GCF is the product of these common prime factors:
GCF = 4
Therefore, the greatest common factor of 24, 144, and 100 is 4.
To find the Greatest Common Factor (GCF) of 24, 144, and 100, we need to find the largest number that evenly divides all three of these numbers.
Step 1: Find the prime factors of each number individually.
Prime factors of 24: 2 * 2 * 2 * 3 = 2^3 * 3
Prime factors of 144: 2 * 2 * 2 * 2 * 3 * 3 = 2^4 * 3^2
Prime factors of 100: 2 * 2 * 5 * 5 = 2^2 * 5^2
Step 2: Determine the common prime factors.
To find the GCF, we need to consider the common prime factors from all three numbers. In this case, the only common prime factor is 2.
Step 3: Determine the lowest power for each common prime factor.
Since 2 is the only common prime factor, we can determine the lowest power of 2 in the given numbers.
From the prime factorization of each number:
- 24 contains 2^3
- 144 contains 2^4
- 100 contains 2^2
The lowest power of 2 is 2^2.
Step 4: Calculate the GCF.
By taking the lowest power of each common prime factor, the GCF of 24, 144, and 100 is 2^2 = 4.
Therefore, the GCF of 24, 144, and 100 is 4.
To find the Greatest Common Factor (GCF) of 24, 144, and 100, we can use the prime factorization method. Here's how:
Step 1: Prime factorize each number.
24 = 2 * 2 * 2 * 3 = 2^3 * 3
144 = 2 * 2 * 2 * 2 * 3 * 3 = 2^4 * 3^2
100 = 2 * 2 * 5 * 5 = 2^2 * 5^2
Step 2: Identify the common prime factors.
Looking at the prime factorizations, we can see that the common prime factors of 24, 144, and 100 are 2 and 3.
Step 3: Multiply the common prime factors.
Multiply the common prime factors we identified: 2 * 2 * 3 = 12
Therefore, the Greatest Common Factor (GCF) of 24, 144, and 100 is 12.