GCF of 32 and 48
GCF of 32 and 48
The Greatest Common Factors (GCF) of 32 and 48 is 16. This is determined by finding the largest numbers that divides both 32 and 48 without leaving a remainder. The prime factorization of 32 is 2⁵ (2 × 2 × 2 × 2 × 2) and the prime factorization of 48 is 2⁴×3 (2 × 2 × 2 × 2 × 3). The highest power of the common prime factor 2 is 2⁴, which is 16, making 16 the GCF of 32 and 48.
GCF of 32 and 48
GCF of 32 and 48 is 16.
Methods to Find GCF of 32 and 48
- Prime Factorization Method
- Long Division Method
- Listing Common Factors
GCF of 32 and 48 by Prime Factorization Method
Prime Factorization of 48:
48 = 2 × 2 × 2 × 2 × 3 (or 2⁴×3)
Identify the Common Prime Factors:
The common prime factor between 32 and 48 is 2.
Determine the Lowest Power of Common Prime Factors:
The lowest power of the common prime factor 2 is 2⁴ (or 16).
Determine the GCF:
Therefore, the GCF of 32 and 48 is 16.
So, the GCF of 32 and 48 is 16.
GCF of 32 and 48 by Long Division Method.
- Divide the larger number (48) by the smaller number (32):
- 48 ÷ 32 gives a quotient of 1 and a remainder of 16.
- Replace the larger number with the smaller number (32) and the smaller number with the remainder (16):
- Now, divide 32 by 16.
- 32 ÷ 16 gives a quotient of 2 and a remainder of 0.
- When the remainder is 0, the divisor at this step is the GCF:
- The last divisor, which is 16, is the GCF.
Therefore, the GCF of 32 and 48 is 16.
GCF of 32 and 48 by Listing Common Factors
List the factors of 32:
Factors of 32: 1, 2, 4, 8, 16, 32
List the factors of 48:
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Identify the common factors:
Common factors of 32 and 48: 1, 2, 4, 8, 16
Determine the greatest common factor:
The greatest common factor is 16.
Therefore, the GCF of 32 and 48 is 16.
What is the GCF of 32 and 48?
The GCF of 32 and 48 is 16.
Why is finding the GCF of 32 and 48 important?
The GCF is useful for simplifying fractions, solving problems involving ratios, and finding common denominators.
Can the GCF of 32 and 48 be found using the Euclidean algorithm?
Yes, the Euclidean algorithm involves repeated division. Divide 48 by 32, get the remainder 16, then divide 32 by 16 to get a remainder of 0. The GCF is 16.
What is the relationship between the GCF and LCM of 32 and 48?
The product of the GCF and LCM of two numbers equals the product of the numbers. For 32 and 48: GCF × LCM = 32 × 48.
Can you find the GCF of 32 and 48 by inspection?
Yes, by observing that both numbers share common factors 1, 2, 4, 8, and 16, you can determine that the largest common factor is 16.
hcf and lcm of 32 and 48
The HCF (Highest Common Factor) of 32 and 48 is 16. The LCM (Least Common Multiple) of 32 and 48 is 96. These values simplify fractions and solve ratio problems effectively.
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