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GCF of 32 and 48

GCF of 32 and 48 is the largest possible number that divides 32 and 48 exactly without any remainder. The factors of 32 and 48 are 1, 2, 4, 8, 16, 32 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There are 3 commonly used methods to find the GCF of 32 and 48 - long division, Euclidean algorithm, and prime factorization.

1. GCF of 32 and 48
2. List of Methods
3. Solved Examples
4. FAQs

What is GCF of 32 and 48?

Answer: GCF of 32 and 48 is 16.

GCF of 32 and 48

Explanation:

The GCF of two non-zero integers, x(32) and y(48), is the greatest positive integer m(16) that divides both x(32) and y(48) without any remainder.

Methods to Find GCF of 32 and 48

Let's look at the different methods for finding the GCF of 32 and 48.

  • Using Euclid's Algorithm
  • Prime Factorization Method
  • Listing Common Factors

GCF of 32 and 48 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 48 and Y = 32

  • GCF(48, 32) = GCF(32, 48 mod 32) = GCF(32, 16)
  • GCF(32, 16) = GCF(16, 32 mod 16) = GCF(16, 0)
  • GCF(16, 0) = 16 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 32 and 48 is 16.

GCF of 32 and 48 by Prime Factorization

GCF of 32 and 48 by Prime Factorization

Prime factorization of 32 and 48 is (2 × 2 × 2 × 2 × 2) and (2 × 2 × 2 × 2 × 3) respectively. As visible, 32 and 48 have common prime factors. Hence, the GCF of 32 and 48 is 2 × 2 × 2 × 2 = 16.

GCF of 32 and 48 by Listing Common Factors

GCF of 32 and 48 by Listing Common Factors
  • Factors of 32: 1, 2, 4, 8, 16, 32
  • Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

There are 5 common factors of 32 and 48, that are 1, 2, 4, 8, and 16. Therefore, the greatest common factor of 32 and 48 is 16.

☛ Also Check:

GCF of 32 and 48 Examples

  1. Example 1: Find the greatest number that divides 32 and 48 exactly.

    Solution:

    The greatest number that divides 32 and 48 exactly is their greatest common factor, i.e. GCF of 32 and 48.
    ⇒ Factors of 32 and 48:

    • Factors of 32 = 1, 2, 4, 8, 16, 32
    • Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

    Therefore, the GCF of 32 and 48 is 16.

  2. Example 2: For two numbers, GCF = 16 and LCM = 96. If one number is 48, find the other number.

    Solution:

    Given: GCF (x, 48) = 16 and LCM (x, 48) = 96
    ∵ GCF × LCM = 48 × (x)
    ⇒ x = (GCF × LCM)/48
    ⇒ x = (16 × 96)/48
    ⇒ x = 32
    Therefore, the other number is 32.

  3. Example 3: Find the GCF of 32 and 48, if their LCM is 96.

    Solution:

    ∵ LCM × GCF = 32 × 48
    ⇒ GCF(32, 48) = (32 × 48)/96 = 16
    Therefore, the greatest common factor of 32 and 48 is 16.

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FAQs on GCF of 32 and 48

What is the GCF of 32 and 48?

The GCF of 32 and 48 is 16. To calculate the GCF of 32 and 48, we need to factor each number (factors of 32 = 1, 2, 4, 8, 16, 32; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the greatest factor that exactly divides both 32 and 48, i.e., 16.

How to Find the GCF of 32 and 48 by Prime Factorization?

To find the GCF of 32 and 48, we will find the prime factorization of the given numbers, i.e. 32 = 2 × 2 × 2 × 2 × 2; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 2, 2 are common terms in the prime factorization of 32 and 48. Hence, GCF(32, 48) = 2 × 2 × 2 × 2 = 16
☛ Prime Number

How to Find the GCF of 32 and 48 by Long Division Method?

To find the GCF of 32, 48 using long division method, 48 is divided by 32. The corresponding divisor (16) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 32, 48?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 32 and 48, i.e. GCF × LCM = 32 × 48.

If the GCF of 48 and 32 is 16, Find its LCM.

GCF(48, 32) × LCM(48, 32) = 48 × 32
Since the GCF of 48 and 32 = 16
⇒ 16 × LCM(48, 32) = 1536
Therefore, LCM = 96
☛ GCF Calculator

What are the Methods to Find GCF of 32 and 48?

There are three commonly used methods to find the GCF of 32 and 48.

  • By Prime Factorization
  • By Listing Common Factors
  • By Long Division
 
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