What is the Greatest Common Factor (GCF) of 16 and 20?
2
4
8
10
The Greatest Common Factor (GCF) of 16 and 20 is the largest factor that both numbers share. To determine this, we list the factors of each number: the factors of 16 are 1, 2, 4, 8, and 16, while the factors of 20 are 1, 2, 4, 5, 10, and 20. The common factors between 16 and 20 are 1, 2, and 4. The largest of these common factors is 4. Therefore, the GCF of 16 and 20 is 4, which is useful for simplifying fractions and solving various mathematical problems involving these numbers.
To find the Greatest Common Factor (GCF) of 16 and 20 using the prime factorization method, follow these steps:
Prime Factorization of Each Number:
Prime factors of 16:
16 = 2 × 2 × 2 × 2
16 = 2⁴
Prime factors of 20:
20 = 2 × 2 × 5
20 = 2² × 5
Identify the Common Prime Factors:
The common prime factor is 2.
The lowest power of the common prime factor is 2².
Multiply the Common Prime Factors:
GCF = 2²
GCF = 4
To find the Greatest Common Factor (GCF) of 16 and 20 using the Long Division Method, follow these steps:
Divide the Larger Number by the Smaller Number:
Divide 20 (larger number) by 16 (smaller number).
20 ÷ 16 = 1 remainder 4
Replace the Larger Number with the Smaller Number:
The divisor (16) becomes the new dividend.
The remainder (4) becomes the new divisor.
Repeat the Division:
Now, divide 16 by 4.
16 ÷ 4 = 4 remainder 0
Check the Remainder:
When the remainder is 0, the current divisors is the GCF.
The remainder is 0, and the current divisor is 4.
To find the Greatest Common Factor (GCF) of 16 and 20 by listing their common factors, follow these steps:
List the Factors of Each Number:
Factors of 16: 1, 2, 4, 8, 16
Factors of 20: 1, 2, 4, 5, 10, 20
Identify the Common Factors:
The common factors of 16 and 20 are: 1, 2, 4
Find the Greatest Common Factor:
The largest number in the list of common factors is 4.
Yes, the Greatest Common Factor (GCF) and the Highest Common Factor (HCF) are the same, which is 4 for 16 and 20.
The GCF helps reduce fractions to their simplest form. For example, 16/20 simplifies to 4/5 when both numerator and denominator are divided by their GCF, which is 4.
The GCF is used to simplify ratios. For example, the ratio 16:20 simplifies to 4:5 by dividing both terms by their GCF, which is 4.
Yes, the GCF is used in solving Diophantine equations, which are equations with integer solutions. Knowing the GCF helps determine if a solution exists and simplifies the process of finding solutions.
The fastest way is often the Euclidean algorithm, which involves a series of divisions until the remainder is 0.
In algebra, the GCF is used to factor out the greatest common factor from terms in an expression, simplifying the expression.
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What is the Greatest Common Factor (GCF) of 16 and 20?
2
4
8
10
Which of the following numbers is a common factor of both 16 and 20?
5
6
8
12
What is the smallest prime factor of the GCF of 16 and 20?
2
3
5
7
How many factors does the GCF of 16 and 20 have?
2
3
4
6
If you subtract the GCF of 16 and 20 from 20, what is the result?
12
14
16
18
What is the result of dividing the GCF of 16 and 20 by 2?
1
2
3
4
Which pair of numbers has the same GCF as 16 and 20?
24 and 30
32 and 40
28 and 36
12 and 18
What is the GCF of 16, 20, and 24?
4
8
12
16
What is the GCF of 16 and 20 when divided by 4?
1
2
3
4
What is the difference between the GCF of 16 and 20 and the number 3?
0
1
2
3
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