What is the greatest common factor of 4, 37 and 51

The Correct Answer and Explanation is:

The greatest common factor (GCF) of 4, 37, and 51 is 1.

✅ Final Answer: 1

🔍 Detailed Explanation

The greatest common factor (GCF)—also called the greatest common divisor (GCD)—is the largest positive number that evenly divides all the given numbers. To find it for 4, 37, and 51, we follow these steps:

Step 1: Prime Factorization

We break each number down into its prime factors:

4 = 2 × 2 (or 222^2)
37 is a prime number, so it cannot be factored further: 37 = 37
51 = 3 × 17

Step 2: Compare Prime Factors

Now list the prime factors:

4: 2
37: 37
51: 3, 17

Clearly, there are no common prime factors shared among all three numbers. Each number has a completely distinct set of prime factors.

Step 3: Conclusion

Because there are no common prime factors, the only number that divides all three is 1. This means the GCF of 4, 37, and 51 is 1.

💡 Why This Matters

When the GCF of a set of numbers is 1, we say the numbers are relatively prime (or coprime) to each other. This doesn’t mean each number is prime, just that they have no shared prime factors.

Understanding GCF is crucial in many areas of mathematics:

Simplifying fractions
Finding least common multiples (LCM)
Solving problems involving ratios
Factoring algebraic expressions

In this case, since the GCF is 1, we can’t simplify any ratios between the numbers further. They are as simplified as possible in relation to each other.

✅ Recap

Prime factorize each number
Identify common factors
Since no common prime factors exist, the GCF = 1

Correct Answer: 1 ✅