what is the GCF of 21 and 30
The greatest common factor (GCF) of 21 and 30 is 3.
To find the greatest common factor (GCF) of two numbers, like 21 and 30, we can use a method called prime factorization. Here is how to do it:
Step 1: Prime factorize both numbers.
- Prime factorization of 21: 3 × 7
- Prime factorization of 30: 2 × 3 × 5
Step 2: Identify the common prime factors.
- Common prime factor(s): 3
Step 3: Multiply the common prime factor(s) to find the GCF.
- GCF of 21 and 30: 3
Therefore, the GCF of 21 and 30 is 3.
To find the Greatest Common Factor (GCF) of 21 and 30, we can use several methods. I will show you two methods: the Prime Factorization method and the Division method.
**Method 1: Prime Factorization**
1. Write the prime factorization of each number.
- Prime factorization of 21: 21 = 3 × 7
- Prime factorization of 30: 30 = 2 × 3 × 5
2. Identify the common prime factors of both numbers. In this case, the common prime factor is 3.
3. Multiply the common prime factors to find the GCF. Therefore, the GCF of 21 and 30 is 3.
**Method 2: Division**
1. List all the factors of both numbers.
- Factors of 21: 1, 3, 7, 21
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
2. Identify the largest factor that both numbers share. In this case, the largest common factor is 3.
3. Therefore, the GCF of 21 and 30 is 3.
Both methods give the same result, which is 3. The GCF of 21 and 30 is 3.