GCF that 28 and 32 is the largest feasible number that divides 28 and also 32 specifically without any kind of remainder. The factors of 28 and 32 are 1, 2, 4, 7, 14, 28 and also 1, 2, 4, 8, 16, 32 respectively. There space 3 generally used techniques to uncover the GCF of 28 and 32 - prime factorization, lengthy division, and also Euclidean algorithm.

You are watching: What is the greatest common factor of 28 and 32

1.GCF of 28 and 32
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF that 28 and also 32 is 4.

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Explanation:

The GCF of two non-zero integers, x(28) and y(32), is the biggest positive essence m(4) that divides both x(28) and y(32) without any kind of remainder.


The approaches to uncover the GCF the 28 and also 32 are described below.

Prime administer MethodUsing Euclid's AlgorithmListing usual Factors

GCF of 28 and also 32 by prime Factorization

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Prime administrate of 28 and 32 is (2 × 2 × 7) and also (2 × 2 × 2 × 2 × 2) respectively. As visible, 28 and also 32 have usual prime factors. Hence, the GCF of 28 and also 32 is 2 × 2 = 4.

GCF that 28 and 32 through Euclidean Algorithm

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

Here X = 32 and also Y = 28

GCF(32, 28) = GCF(28, 32 mode 28) = GCF(28, 4)GCF(28, 4) = GCF(4, 28 mode 4) = GCF(4, 0)GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, wherein X ≠ 0)

Therefore, the worth of GCF the 28 and also 32 is 4.

GCF that 28 and also 32 by Listing usual Factors

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Factors that 28: 1, 2, 4, 7, 14, 28Factors of 32: 1, 2, 4, 8, 16, 32

There are 3 common factors of 28 and also 32, that space 1, 2, and also 4. Therefore, the greatest usual factor the 28 and also 32 is 4.

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GCF the 28 and also 32 Examples


Example 1: discover the GCF of 28 and also 32, if your LCM is 224.

Solution:

∵ LCM × GCF = 28 × 32⇒ GCF(28, 32) = (28 × 32)/224 = 4Therefore, the greatest typical factor the 28 and also 32 is 4.


Example 2: The product of 2 numbers is 896. If their GCF is 4, what is your LCM?

Solution:

Given: GCF = 4 and also product of number = 896∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 896/4Therefore, the LCM is 224.


Example 3: discover the greatest number that divides 28 and also 32 exactly.

Solution:

The greatest number that divides 28 and 32 precisely is their greatest usual factor, i.e. GCF that 28 and also 32.⇒ factors of 28 and 32:

Factors that 28 = 1, 2, 4, 7, 14, 28Factors the 32 = 1, 2, 4, 8, 16, 32

Therefore, the GCF that 28 and also 32 is 4.


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FAQs ~ above GCF of 28 and also 32

What is the GCF of 28 and 32?

The GCF of 28 and also 32 is 4. To calculate the GCF the 28 and also 32, we need to element each number (factors that 28 = 1, 2, 4, 7, 14, 28; components of 32 = 1, 2, 4, 8, 16, 32) and also choose the greatest variable that exactly divides both 28 and 32, i.e., 4.

What is the Relation in between LCM and GCF of 28, 32?

The complying with equation can be supplied to refer the relation in between Least usual Multiple and GCF of 28 and also 32, i.e. GCF × LCM = 28 × 32.

If the GCF the 32 and 28 is 4, discover its LCM.

GCF(32, 28) × LCM(32, 28) = 32 × 28Since the GCF of 32 and also 28 = 4⇒ 4 × LCM(32, 28) = 896Therefore, LCM = 224☛ GCF Calculator

How to find the GCF the 28 and also 32 through Long division Method?

To uncover the GCF the 28, 32 using long division method, 32 is divided by 28. The corresponding divisor (4) when remainder equates to 0 is taken as GCF.

See more: A Maritime Polar Air Mass Is A Cold Air Mass That Forms Over Which Two Oceans?

What room the approaches to discover GCF the 28 and also 32?

There room three generally used techniques to uncover the GCF the 28 and also 32.

By lengthy DivisionBy Euclidean AlgorithmBy prime Factorization

How to discover the GCF the 28 and also 32 by element Factorization?

To uncover the GCF the 28 and 32, we will discover the prime factorization the the offered numbers, i.e. 28 = 2 × 2 × 7; 32 = 2 × 2 × 2 × 2 × 2.⇒ due to the fact that 2, 2 are usual terms in the prime factorization the 28 and 32. Hence, GCF(28, 32) = 2 × 2 = 4☛ What room Prime Numbers?