GCF of 12 and 16
GCF of 12 and 16
To find the GCF (Greatest Common Factor) of 12 and 16, we start by listing the factors of each number. The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 16 are 1, 2, 4, 8, and 16. The common factors between these two numbers are 1, 2, and 4. The greatest of these common factors is 4. Therefore, the GCF of 12 and 16 is 4, meaning that 4 is the largest numbers that can divide both 12 and 16 without leaving a remainder.
GCF of 12 and 16
GCF of 12 and 16 is 4.
Methods to Find GCF of 12 and 16
- Prime Factorization Method
- Long Division Method
- Listing Common Factors
GCF of 12 and 16 by Prime Factorization Method
Prime Factorization:
12: The prime factors of 12 are 2 and 3.
12 = 2 × 2 × 3
16: The prime factors of 16 are all 2.
16 = 2 × 2 × 2 × 2
Identify Common Factors:
The common prime factors between 12 and 16 are 2 and 2.
Calculate the GCF:
Multiply the common prime factors together.
GCF = 2 × 2 =4
Therefore, the GCF of 12 and 16 using the prime factorization method is 4.
GCF of 12 and 16 by Long Division Method.
Divide the larger number by the smaller number:
Divide 16 by 12.
16 ÷ 12 = 1 remainder 4
Replace the larger number with the smaller number and the smaller number with the remainder:
Now, divide 12 by the remainder 4.
12 ÷ 4 = 3 remainder 0
Continue the process until the remainder is 0:
Since the remainder is now 0, the divisor at this step is the GCF.
Therefore, the GCF of 12 and 16 using the long division method is 4.
GCF of 12 and 16 by Listing Common Factors
GCF of 12 and 16 by Listing Common Factors
List the factors of each number:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 16: 1, 2, 4, 8, 16
Identify the common factors:
Common factors of 12 and 16: 1, 2, 4
Determine the greatest common factor:
The largest common factor is 4.
Therefore, the GCF of 12 and 16 by listing common factors is 4.
What is the GCF of 12 and 16?
The GCF of 12 and 16 is 4.
How does finding the GCF help in simplifying fractions?
The GCF is used to simplify fractions by dividing the numerator and the denominator by the GCF.
Are 12 and 16 relatively prime?
No, they are not relatively prime because their GCF is 4, not 1.
Can the GCF of two numbers be one of the numbers?
Yes, the GCF can be one of the numbers if one number is a multiple of the other. However, for 12 and 16, the GCF is 4, which is not one of the numbers.
How do you verify the GCF of 12 and 16?
To verify, check the divisors. Divide both numbers by 4 to see that 4 is the largest number that divides both 12 and 16 without a remainder, confirming the GCF is correct.
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