GCF of 9 and 15
GCF of 9 and 15
To find the Greatest Common Factor (GCF) of 9 and 15, you can use several methods such as listing common factors, prime factorization, and the long division method. By listing the factors, we see that the numbers factors of 9 are 1, 3, and 9, while the factors of 15 are 1, 3, 5, and 15. The common factors are 1 and 3, with the greatest common factor being 3. Using the prime factorization method, 9 is 3² and 15 is 3 × 5, with the common prime factor being 3. Using the long division method, dividing 15 by 9 gives a remainder of 6, then dividing 9 by 6 gives a remainder of 3, and finally dividing 6 by 3 gives a remainder of 0, confirming that the GCF is 3. Thus, the GCF of 9 and 15 is 3.
GCF of 9 and 15
GCF of 9 and 15 is 3 .
Methods to Find GCF of 9 and 15
- Prime Factorization Method
- Long Division Method
- Listing Common Factors
GCF of 9 and 15 by Prime Factorization Method.
To find the Greatest Common Factor (GCF) of 9 and 15 using the prime factorization method, follow these steps:
Step 1: Find the prime factorization of each number
Prime factorization of 9:
9 = 3 × 3 = 3²
Prime factorization of 15:
15 = 3 × 5
Step 2: Identify the common prime factors
The only common prime factor of 9 and 15 is 3.
Step 3: Multiply the common prime factors
Since the only common prime factor is 3, the GCF is 3.
GCF of 9 and 15 by Long Division Method.
To find the Greatest Common Factor (GCF) of 9 and 15 using the long division method, follow these steps:
Step 1: Divide the larger number by the smaller number
15 ÷ 9 = 1 with a remainder of 6.
Step 2: Replace the larger number with the smaller number, and the smaller number with the remainder
Now, we have 9 and 6.
Step 3: Repeat the division
9 ÷ 6 = 1 with a remainder of 3.
Step 4: Continue the process
6 ÷ 3 = 2 with a remainder of 0.
Step 5: When the remainder is 0, the divisors is the GCF
The last non-zero remainder is 3. So, the GCF of 9 and 15 is 3.
GCF of 9 and 15 by Listing Common Factors.
To find the Greatest Common Factor (GCF) of 9 and 15 by listing common factors, follow these steps:
Step 1: List the factors of each number
Factors of 9:
1, 3, 9
Factors of 15:
1, 3, 5, 15
Step 2: Identify the common factors
Common factors of 9 and 15:
1, 3
Step 3: Determine the greatest common factor
The largest common factor is 3. Therefore, the GCF of 9 and 15 is 3.
How do you find the GCF of 9 and 15?
Use methods like long division, listing common factors, and prime factorization.
What are the factors of 9?
The factors of 9 are 1, 3, and 9.
How does the GCF help in simplifying fractions?
The GCF can be used to divide both the numerator and the denominator to simplify a fraction.
Is the GCF of 9 and 15 a prime number?
Yes, 3 is a prime number.
Can the GCF of 9 and 15 be one of the numbers?
Yes, if one number is a multiple of the other. For 9 and 15, the GCF is 3.
What is the least common multiple (LCM) of 9 and 15?
The LCM of 9 and 15 is 45.
Are 9 and 15 relatively prime?
No, because their GCF is 3, not 1.
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