What Is The Greatest Common Factor Of 9 And 15?

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Introduction

In mathematics, the greatest common factor (GCF) is the largest number that divides two or more integers without leaving any remainder. It is also known as the greatest common divisor (GCD). When finding the GCF, the numbers should be factored into their prime factors.

Understanding the Factors of 9 and 15

To find the GCF of 9 and 15, we need to factor both numbers. The factors of 9 are 1, 3, and 9, while the factors of 15 are 1, 3, 5, and 15. It is important to note that 9 and 15 have a common factor of 3 since both numbers have 3 as one of their factors.

Using Prime Factorization to Find the GCF

Prime factorization is the process of breaking down a number into its prime factors. To find the GCF of 9 and 15, we need to find the prime factors of both numbers. The prime factors of 9 are 3 x 3, while the prime factors of 15 are 3 x 5.

Step-by-Step Solution

1. Write down the factors of 9 and 15. 2. Identify the common factors of 9 and 15. 3. Write down the prime factors of 9 and 15. 4. Identify the common prime factors of 9 and 15. 5. Multiply the common prime factors to find the GCF.

Calculating the GCF of 9 and 15

Since both 9 and 15 share the common factor of 3, we can use prime factorization to find the GCF. The common prime factors of 9 and 15 are 3, which means that the GCF of 9 and 15 is 3.

Conclusion

To summarize, the greatest common factor of 9 and 15 is 3. It is important to factor the numbers into their prime factors to find the GCF. The GCF is useful in simplifying fractions and finding the lowest common denominator.