GCF of 28 and 64 is the largest feasible number that divides 28 and also 64 exactly without any kind of remainder. The components of 28 and 64 room 1, 2, 4, 7, 14, 28 and 1, 2, 4, 8, 16, 32, 64 respectively. There room 3 generally used approaches to discover the GCF of 28 and 64 - long division, prime factorization, and Euclidean algorithm.

You are watching: What is the gcf of 28 and 64

1.GCF that 28 and 64
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF of 28 and 64 is 4.

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Explanation:

The GCF of 2 non-zero integers, x(28) and y(64), is the biggest positive essence m(4) the divides both x(28) and also y(64) without any type of remainder.


The techniques to discover the GCF the 28 and 64 are explained below.

Listing usual FactorsLong division MethodPrime administer Method

GCF of 28 and also 64 through Listing typical Factors

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Factors of 28: 1, 2, 4, 7, 14, 28Factors of 64: 1, 2, 4, 8, 16, 32, 64

There room 3 common factors the 28 and 64, that room 1, 2, and also 4. Therefore, the greatest usual factor the 28 and 64 is 4.

GCF that 28 and also 64 by long Division

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GCF the 28 and also 64 is the divisor the we get when the remainder i do not care 0 after doing long division repeatedly.

Step 2: because the remainder ≠ 0, we will certainly divide the divisor of action 1 (28) through the remainder (8).Step 3: Repeat this process until the remainder = 0.

The matching divisor (4) is the GCF that 28 and 64.

GCF the 28 and 64 by element Factorization

Prime administrate of 28 and also 64 is (2 × 2 × 7) and also (2 × 2 × 2 × 2 × 2 × 2) respectively. Together visible, 28 and also 64 have usual prime factors. Hence, the GCF the 28 and also 64 is 2 × 2 = 4.

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GCF that 28 and 64 Examples


Example 1: discover the biggest number the divides 28 and 64 exactly.

Solution:

The biggest number the divides 28 and also 64 exactly is their greatest typical factor, i.e. GCF that 28 and also 64.⇒ determinants of 28 and 64:

Factors of 28 = 1, 2, 4, 7, 14, 28Factors the 64 = 1, 2, 4, 8, 16, 32, 64

Therefore, the GCF of 28 and 64 is 4.


Example 2: The product of 2 numbers is 1792. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and also product of numbers = 1792∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 1792/4Therefore, the LCM is 448.


Example 3: For two numbers, GCF = 4 and also LCM = 448. If one number is 64, uncover the various other number.

Solution:

Given: GCF (z, 64) = 4 and also LCM (z, 64) = 448∵ GCF × LCM = 64 × (z)⇒ z = (GCF × LCM)/64⇒ z = (4 × 448)/64⇒ z = 28Therefore, the other number is 28.


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FAQs ~ above GCF that 28 and also 64

What is the GCF the 28 and 64?

The GCF of 28 and 64 is 4. To calculation the GCF (Greatest common Factor) of 28 and also 64, we need to element each number (factors the 28 = 1, 2, 4, 7, 14, 28; determinants of 64 = 1, 2, 4, 8, 16, 32, 64) and also choose the greatest element that specifically divides both 28 and 64, i.e., 4.

If the GCF that 64 and also 28 is 4, uncover its LCM.

GCF(64, 28) × LCM(64, 28) = 64 × 28Since the GCF that 64 and 28 = 4⇒ 4 × LCM(64, 28) = 1792Therefore, LCM = 448☛ GCF Calculator

How to find the GCF of 28 and 64 through Long department Method?

To find the GCF the 28, 64 utilizing long department method, 64 is separated by 28. The equivalent divisor (4) when remainder amounts to 0 is taken as GCF.

What are the techniques to discover GCF of 28 and 64?

There space three typically used methods to discover the GCF of 28 and 64.

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By Listing typical FactorsBy lengthy DivisionBy element Factorization

What is the Relation in between LCM and GCF that 28, 64?

The following equation can be offered to to express the relation between Least usual Multiple (LCM) and also GCF that 28 and 64, i.e. GCF × LCM = 28 × 64.

How to uncover the GCF of 28 and 64 by prime Factorization?

To find the GCF that 28 and also 64, we will uncover the element factorization the the offered numbers, i.e. 28 = 2 × 2 × 7; 64 = 2 × 2 × 2 × 2 × 2 × 2.⇒ because 2, 2 are common terms in the prime factorization of 28 and also 64. Hence, GCF(28, 64) = 2 × 2 = 4☛ What is a prime Number?