What is the Greatest Common Factor (GCF) of 16 and 24?
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GCF of 16 and 24 – How to find in Different Ways
GCF of 16 and 24 – How to find in Different Ways
To find the greatest common factor (GCF) of 16 and 24, we can employ various methods. One approach is through listing common factors, which includes identifying numbers that divide evenly into both 16 and 24. The common factors of 16 are 1, 2, 4, 8, and 16, while those of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Among these, the largest common factor is 8. Another method is prime factorization, where we break down 16 into 2×2×2×2 and 24 into 2×2×2×3, and then identify the common prime factors, resulting in 2×2×2=8. Thus, the greatest common factor of 16 and 24 is 8.
GCF of 16 and 24
GCF of 16 and 24 is 8.
The greatest common factor (GCF) of 16 and 24 is 8. By listing their common factors, which include 1, 2, 4, and 8, 8 emerges as the largest number dividing both without remainder, making it the GCF.
Methods to Find GCF of 16 and 24
- Prime Factorization Method
- Long Division Method
- Listing Common Factors
GCF of 16 and 24 by Prime Factorization Method
Prime factorization of 16: 16=2×2×2×2
Prime factorization of 24: 24=2×2×2×3
Both 16 and 24 have a common prime factor: 2
The GCF is found by multiplying this common prime factor: 2×2×2=8
Hence, the GCF of 16 and 24 is 8.
GCF of 16 and 24 by Long Division Method.
Step 1: Divide the larger number (24) by the smaller number (16).
24 ÷ 16 =1 with a remainder of 8
Step 2: Since the remainder (8) is not 0, repeat the process by dividing the divisor (16) by the remainder (8).
16 ÷ 8 = 2 with no remainder
Step 3: Since the remainder is now 0, we stop. The divisor from the last division, which is 8, is the greatest common factor (GCF) of 16 and 24.
Therefore, the GCF of 16 and 24 by the long division method is 8.
GCF of 16 and 24 by Listing Common Factors
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
To find the greatest common factor (GCF) of 16 and 24 by listing common factors, we identify numbers that divide evenly into both. The common factors of 16 are 1, 2, 4, 8, and 16, while those of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Among these, the largest common factor is 8. Therefore, the GCF of 16 and 24 by listing common factors is 8.
What are the common factors of 16 and 24?
Common factors of 16 and 24 include 1, 2, 4, and 8.
What is the significance of 8 as the GCF of 16 and 24?
It’s the largest number that divides both 16 and 24 without leaving a remainder.
How can the GCF of 16 and 24 be used in real-world scenarios?
It can aid in tasks involving proportions, scaling, and simplification of measurements or dimensions.
What is the GCF and LCM of 24 16?
The GCF (Greatest Common Factor) of 24 and 16 is 8. The LCM (Least Common Multiple) of 24 and 16 is 48.
What’s the least common factor of 16 and 24?
The least common factor of 16 and 24 is 1, as it’s the smallest positive integer that divides both numbers without leaving a remainder.
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Practice Test
Which of the following is a common factor of both 16 and 24?
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How many common factors do 16 and 24 have?
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What is the smallest common factor of 16 and 24?
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Which of the following numbers is not a common factor of both 16 and 24?
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The GCF of 16 and 24 is a factor of which of the following numbers?
12
32
48
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If you multiply the GCF of 16 and 24 by 2, what do you get?
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16
24
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Which of the following pairs of numbers has the same GCF as 16 and 24?
8 and 12
12 and 18
10 and 20
32 and 48
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What is the GCF of 16, 24, and 32?
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The sum of the GCF of 16 and 24 and the smallest prime number is:
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