What is the Greatest Common Factor (GCF) of 24 and 32?
4
8
12
16
The Greatest Common Factor (GCF) of 24 and 32 is determined by finding the largest factor that both numbers share. First, list the factors of each number: for 24, the factors are 1, 2, 3, 4, 6, 8, 12, and 24, while for 32, the factors are 1, 2, 4, 8, 16, and 32. The common factors are 1, 2, 4, and 8. The largest of these common factors is 8. Therefore, the GCF of 24 and 32 is 8.
To find the Greatest Common Factor (GCF) of 24 and 32 using the prime factorization method, follow these steps:
Prime Factorization of Each Number:
Prime factors of 24:
24 = 2 × 2 × 2 × 3
24 = 2³ × 3
Prime factors of 32:
32 = 2 × 2 × 2 × 2 × 2
32 = 2⁵
Identify the Common Prime Factors:
The common prime factor is 2.
The lowest power of the common prime factor is 2³.
Multiply the Common Prime Factors:
GCF = 2³
GCF = 8
Divide the Larger Number by the Smaller Number:
Divide 32 (larger number) by 24 (smaller number).
32 ÷ 24 = 1 remainder 8
Replace the Larger Number with the Smaller Number:
The divisor (24) becomes the new dividend.
The remainder (8) becomes the new divisor.
Repeat the Division:
Now, divide 24 by 8.
24 ÷ 8 = 3 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 8.
List the Factors of Each Number:
Identify the Common Factors:
Find the Greatest Common Factor:
The largest number in the list of common factors is 8.
The Greatest Common Factor (GCF) of 24 and 32 is 8, and the Least Common Multiple (LCM) of 24 and 32 is 96. These values are crucial for simplifying fractions and solving ratio problems.
The greatest GCF of 24 and 32 is 8. This value represents the largest factor that both numbers share, essential for simplifying fractions and solving various mathematical problems.
Yes, the Euclidean algorithm involves repeated division. Divide 32 by 24, get the remainder 8, then divide 24 by 8 to get a remainder of 0. The GCF is 8.
It helps in tasks such as simplifying recipes, splitting objects into equal parts, and solving problems involving proportions or ratios.
The GCF helps reduce fractions to their simplest form. For example, 24/32 simplifies to 3/4 when both numerator and denominator are divided by their GCF, which is 8.
The GCF is used to simplify ratios. For example, the ratio 24:32 simplifies to 3:4 by dividing both terms by their GCF, which is 8.
The Greatest Common Factor (GCF) of 24 and 32 is determined by finding the largest factor that both numbers share. First, list the factors of each number: for 24, the factors are 1, 2, 3, 4, 6, 8, 12, and 24, while for 32, the factors are 1, 2, 4, 8, 16, and 32. The common factors are 1, 2, 4, and 8. The largest of these common factors is 8. Therefore, the GCF of 24 and 32 is 8.
Prime Factorization Method
Long Division Method
Listing Common Factors
To find the Greatest Common Factor (GCF) of 24 and 32 using the prime factorization method, follow these steps:
Prime Factorization of Each Number:
Prime factors of 24:
24 = 2 × 2 × 2 × 3
24 = 2³ × 3
Prime factors of 32:
32 = 2 × 2 × 2 × 2 × 2
32 = 2⁵
Identify the Common Prime Factors:
The common prime factor is 2.
The lowest power of the common prime factor is 2³.
Multiply the Common Prime Factors:
GCF = 2³
GCF = 8
Divide the Larger Number by the Smaller Number:
Divide 32 (larger number) by 24 (smaller number).
32 ÷ 24 = 1 remainder 8
Replace the Larger Number with the Smaller Number:
The divisor (24) becomes the new dividend.
The remainder (8) becomes the new divisor.
Repeat the Division:
Now, divide 24 by 8.
24 ÷ 8 = 3 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 8.
List the Factors of Each Number:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 32: 1, 2, 4, 8, 16, 32
Identify the Common Factors:
The common factors of 24 and 32 are: 1, 2, 4, 8
Find the Greatest Common Factor:
The largest number in the list of common factors is 8.
The Greatest Common Factor (GCF) of 24 and 32 is 8, and the Least Common Multiple (LCM) of 24 and 32 is 96. These values are crucial for simplifying fractions and solving ratio problems.
The greatest GCF of 24 and 32 is 8. This value represents the largest factor that both numbers share, essential for simplifying fractions and solving various mathematical problems.
Yes, the Euclidean algorithm involves repeated division. Divide 32 by 24, get the remainder 8, then divide 24 by 8 to get a remainder of 0. The GCF is 8.
It helps in tasks such as simplifying recipes, splitting objects into equal parts, and solving problems involving proportions or ratios.
The GCF helps reduce fractions to their simplest form. For example, 24/32 simplifies to 3/4 when both numerator and denominator are divided by their GCF, which is 8.
The GCF is used to simplify ratios. For example, the ratio 24:32 simplifies to 3:4 by dividing both terms by their GCF, which is 8.
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What is the Greatest Common Factor (GCF) of 24 and 32?
4
8
12
16
Which of the following is a common factor of 24 and 32?
6
7
8
10
How many factors does the GCF of 24 and 32 have?
2
3
4
5
Which number is the largest common factor of 24 and 32?
4
6
8
12
What is the smallest prime factor of the GCF of 24 and 32?
2
3
5
7
Which of these pairs of numbers has the same GCF as 24 and 32?
16 and 24
32 and 40
48 and 64
24 and 36
The GCF of 24 and 32 is also a factor of which of the following numbers?
32
40
48
64
What is the GCF of 24 and 32 multiplied by 5?
40
48
50
80
The GCF of 24 and 32 is subtracted from 24. What is the result?
8
12
16
20
What is the difference between the GCF of 24 and 32 and the number 6?
1
2
4
6
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