GCF (630, 450)
The Greatest Common Factor (GCF) of 630 and 450 is 90.
To find the greatest common factor (GCF) of 630 and 450, we can use several methods. Here is one common method:
Step 1: Find the prime factorization of each number.
630: Divide 630 by its smallest prime factor, which is 2. The result is 315.
Divide 315 by its smallest prime factor, which is 3. The result is 105.
Divide 105 by its smallest prime factor, which is 3. The result is 35.
Divide 35 by its smallest prime factor, which is 5. The result is 7.
Divide 7 by its smallest prime factor, which is 7. The result is 1.
Therefore, the prime factorization of 630 is 2 * 3 * 3 * 5 * 7.
450: Divide 450 by its smallest prime factor, which is 2. The result is 225.
Divide 225 by its smallest prime factor, which is 3. The result is 75.
Divide 75 by its smallest prime factor, which is 3. The result is 25.
Divide 25 by its smallest prime factor, which is 5. The result is 5.
Divide 5 by its smallest prime factor, which is 5. The result is 1.
Therefore, the prime factorization of 450 is 2 * 3 * 3 * 5 * 5.
Step 2: Identify the common prime factors.
From the prime factorizations, we can see that the common prime factors between 630 and 450 are 2, 3, and 5.
Step 3: Multiply the common prime factors.
To find the GCF, multiply the common prime factors: GCF = 2 * 3 * 5 = 30.
Therefore, the GCF of 630 and 450 is 30.
To find the greatest common factor (GCF) of two numbers, such as 630 and 450, you can use several methods. One method is to list all the factors of each number and find the largest one that they have in common. Another method is to use prime factorization.
Let's go with the prime factorization method:
Step 1: Prime factorize both numbers:
630:
Divide 630 by the smallest prime number possible, which is 2. We get 315.
Divide 315 by 3. We get 105.
Divide 105 by 3. We get 35.
Divide 35 by 5. We get 7.
Hence, the prime factorization of 630 is 2 * 3 * 3 * 5 * 7.
450:
Divide 450 by 2. We get 225.
Divide 225 by 3. We get 75.
Divide 75 by 3. We get 25.
Divide 25 by 5. We get 5.
Hence, the prime factorization of 450 is 2 * 3 * 3 * 5 * 5.
Step 2: Identify the common prime factors in both numbers:
The common prime factors are 2, 3, and 5.
Step 3: Multiply the common prime factors together:
2 * 3 * 5 = 30.
Therefore, the GCF of 630 and 450 is 30.