What is the GCF of 9 and 18?
3
6
9
18
The Greatest Common Factor (GCF) of 9 and 18 is determined by finding the largest factor that both numbers share. First, list the factors of each number: for 9, the factors are 1, 3, and 9, while for 18, the factors are 1, 2, 3, 6, 9, and 18. The common factors are 1, 3, and 9. The largest of these common factors is 9. Therefore, the GCF of 9 and 18 is 9, making it useful for simplifying fractions and solving ratio problems involving these numbers.
Prime Factorization of Each Number:
Prime factors of 9:
9 = 3 × 3
9 = 3²
Prime factors of 18:
18 = 2 × 3 × 3
18 = 2 × 3²
Identify the Common Prime Factors:
The common prime factor is 3.
The lowest power of the common prime factor is 3².
Multiply the Common Prime Factors:
GCF = 3²
GCF = 9
Divide the Larger Number by the Smaller Number:
Divide 18 (larger number) by 9 (smaller number).
18 ÷ 9 = 2 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 9.
List the Factors of Each Number:
Factors of 9: 1, 3, 9
Factors of 18: 1, 2, 3, 6, 9, 18
Identify the Common Factors:
The common factors of 9 and 18 are: 1, 3, 9
Find the Greatest Common Factor:
The largest number in the list of common factors is 9.
The GCF is useful for simplifying fractions, solving problems involving ratios, and finding common denominators.
Yes, many online calculators can find the GCF of two numbers. Enter 9 and 18, and the calculator will return 9.
Yes, the Euclidean algorithm involves repeated division. Divide 18 by 9 to get a remainder of 0. The GCF is 9.
Yes, the Greatest Common Factor (GCF) and the Highest Common Factor (HCF) are the same, which is 9 for 9 and 18.
The GCF helps reduce fractions to their simplest form. For example, 9/18 simplifies to 1/2 when both numerator and denominator are divided by their GCF, which is 9.
The Least Common Multiple (LCM) of 9 and 18 is 18. It is the smallest number that is a multiple of both 9 and 18, useful for adding and comparing fractions.
The Greatest Common Factor (GCF) of 9 and 18 is determined by finding the largest factor that both numbers share. First, list the factors of each number: for 9, the factors are 1, 3, and 9, while for 18, the factors are 1, 2, 3, 6, 9, and 18. The common factors are 1, 3, and 9. The largest of these common factors is 9. Therefore, the GCF of 9 and 18 is 9, making it useful for simplifying fractions and solving ratio problems involving these numbers.
Prime Factorization Method
Long Division Method
Listing Common Factors
Prime Factorization of Each Number:
Prime factors of 9:
9 = 3 × 3
9 = 3²
Prime factors of 18:
18 = 2 × 3 × 3
18 = 2 × 3²
Identify the Common Prime Factors:
The common prime factor is 3.
The lowest power of the common prime factor is 3².
Multiply the Common Prime Factors:
GCF = 3²
GCF = 9
Divide the Larger Number by the Smaller Number:
Divide 18 (larger number) by 9 (smaller number).
18 ÷ 9 = 2 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 9.
List the Factors of Each Number:
Factors of 9: 1, 3, 9
Factors of 18: 1, 2, 3, 6, 9, 18
Identify the Common Factors:
The common factors of 9 and 18 are: 1, 3, 9
Find the Greatest Common Factor:
The largest number in the list of common factors is 9.
The GCF is useful for simplifying fractions, solving problems involving ratios, and finding common denominators.
Yes, many online calculators can find the GCF of two numbers. Enter 9 and 18, and the calculator will return 9.
Yes, the Euclidean algorithm involves repeated division. Divide 18 by 9 to get a remainder of 0. The GCF is 9.
Yes, the Greatest Common Factor (GCF) and the Highest Common Factor (HCF) are the same, which is 9 for 9 and 18.
The GCF helps reduce fractions to their simplest form. For example, 9/18 simplifies to 1/2 when both numerator and denominator are divided by their GCF, which is 9.
The Least Common Multiple (LCM) of 9 and 18 is 18. It is the smallest number that is a multiple of both 9 and 18, useful for adding and comparing fractions.
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What is the GCF of 9 and 18?
3
6
9
18
Which of the following is a common factor of 9 and 18?
2
3
4
5
How many factors does the GCF of 9 and 18 have?
1
2
3
4
What is the smallest prime factor of the GCF of 9 and 18?
2
3
5
7
Which of these pairs of numbers has the same GCF as 9 and 18?
12 and 18
15 and 30
18 and 27
24 and 36
If you add the GCF of 9 and 18 to the number 5, what is the result?
14
15
16
17
The GCF of 9 and 18 is also a factor of which of the following numbers?
18
24
30
36
What is the GCF of 9 and 18 multiplied by 4?
36
45
72
81
What is the result of dividing the GCF of 9 and 18 by 3?
1
2
3
4
The GCF of 9 and 18 is subtracted from 18. What is the result?
9
10
12
15
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