Find the GCF of the numbers.
120, 1000, 2250
A) 20
B) 10
C) 30
D) 50
If you don't know the right answer, try eliminating choices that are wrong. For example, 50 cannot be the GCF for 120.
how am i going to do that
To find the greatest common factor (GCF) of the numbers 120, 1000, and 2250, we can use the method of prime factorization. Here's how to do it step by step:
1. Start by finding the prime factors of each number:
- For 120: Prime factors are 2 × 2 × 2 × 3 × 5, which can be written as 2³ × 3 × 5.
- For 1000: Prime factors are 2 × 2 × 2 × 5 × 5 × 5, which can be written as 2³ × 5³.
- For 2250: Prime factors are 2 × 3 × 3 × 5 × 5, which can be written as 2 × 3² × 5².
2. Identify the common prime factors of the numbers. In this case, the common prime factors are 2, 3, and 5.
3. Find the smallest exponent for each common prime factor:
- Exponent of 2: Minimum exponent is 1 (from 2³ × 3 × 5).
- Exponent of 3: Minimum exponent is 1 (from 2 × 3² × 5²).
- Exponent of 5: Minimum exponent is 1 (from 2 × 3 × 5²).
4. Multiply the common prime factors with their smallest exponent: 2 × 3 × 5 = 30.
Therefore, the GCF of 120, 1000, and 2250 is 30.
So, the correct answer is C) 30.