GCF of 8 and 10
GCF of 8 and 10
The Greatest Common Factors (GCF) of 8 and 10 is 2. This is determined by identifying the largest numbers that divides both 8 and 10 without leaving a remainder. The prime factorization of 8 is 2³ (2 × 2 × 2) and the prime factorization of 10 is 2 × 5. The only common prime factor is 2, making it the GCF of 8 and 10.
GCF of 8 and 10
GCF of 8 and 10 is 2.
Methods to Find GCF of 8 and 10
- Prime Factorization Method
- Long Division Method
- Listing Common Factors
GCF of 8 and 10 by Prime Factorization Method
Prime Factorization of 8:
- 8 = 2 × 2 × 2 (or 2³)
Prime Factorization of 10:
- 10 = 2 × 5
Identify Common Factors:
- The common prime factor between 8 and 10 is 2.
Determine the GCF:
- Since the only common prime factor is 2, the GCF of 8 and 10 is 2.
GCF of 8 and 10 by Long Division Method.
Divide the larger number (10) by the smaller number (8):
10 ÷ 8 gives a quotient of 1 and a remainder of 2.
Replace the larger number with the smaller number (8) and the smaller number with the remainder (2):
Now, divide 8 by 2.
8 ÷ 2 gives a quotient of 4 and a remainder of 0.
When the remainder is 0, the divisor at this step is the GCF:
The last divisor, which is 2, is the GCF.
Therefore, the GCF of 8 and 10 is 2.
GCF of 8 and 10 by Listing Common Factors
List the factors of 8:
Factors of 8: 1, 2, 4, 8
List the factors of 10:
Factors of 10: 1, 2, 5, 10
Identify the common factors:
Common factors of 8 and 10: 1, 2
Determine the greatest common factor:
The greatest common factor is 2.
Therefore, the GCF of 8 and 10 is 2.
Why is the GCF of 8 and 10 important?
The GCF is important for simplifying fractions, solving problems involving ratios, and finding common denominators.
Can the GCF of 8 and 10 be greater than 2?
No, the GCF of 8 and 10 cannot be greater than 2 because 2 is the largest number that divides both 8 and 10 without leaving a remainder.
How is the GCF of 8 and 10 used in real-life situations?
The GCF is used in real-life situations such as dividing items into smaller sections, comparing quantities, and simplifying mathematical problems involving fractions.
Can the GCF of 8 and 10 be found using a calculator?
Yes, many calculators have a function to find the GCF of two numbers. Simply input the numbers 8 and 10 and use the GCF or GCD function.
What is 8 and 10 lowest common factor?
The lowest common factor of 8 and 10 is 1, as it is the smallest positive integer that divides both numbers without leaving a remainder.
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