GCF of 64 and also 32 is the largest feasible number the divides 64 and also 32 specifically without any remainder. The components of 64 and 32 space 1, 2, 4, 8, 16, 32, 64 and also 1, 2, 4, 8, 16, 32 respectively. There space 3 commonly used approaches to uncover the GCF the 64 and also 32 - lengthy division, prime factorization, and Euclidean algorithm.

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1.GCF of 64 and 32
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF that 64 and 32 is 32.

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Explanation:

The GCF of 2 non-zero integers, x(64) and y(32), is the best positive integer m(32) the divides both x(64) and y(32) without any kind of remainder.


Let's look in ~ the different methods for finding the GCF the 64 and also 32.

Prime administer MethodListing usual FactorsLong department Method

GCF that 64 and also 32 by element Factorization

Prime administer of 64 and also 32 is (2 × 2 × 2 × 2 × 2 × 2) and also (2 × 2 × 2 × 2 × 2) respectively. As visible, 64 and 32 have common prime factors. Hence, the GCF the 64 and also 32 is 2 × 2 × 2 × 2 × 2 = 32.

GCF of 64 and 32 by Listing common Factors

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Factors the 64: 1, 2, 4, 8, 16, 32, 64Factors of 32: 1, 2, 4, 8, 16, 32

There are 6 common factors that 64 and 32, that are 32, 1, 2, 4, 8, and also 16. Therefore, the greatest usual factor the 64 and 32 is 32.

GCF the 64 and also 32 by lengthy Division

GCF the 64 and also 32 is the divisor the we obtain when the remainder becomes 0 after doing long department repeatedly.

Step 2: since the remainder = 0, the divisor (32) is the GCF the 64 and also 32.

The matching divisor (32) is the GCF the 64 and also 32.

☛ also Check:


GCF that 64 and 32 Examples


Example 1: For two numbers, GCF = 32 and LCM = 64. If one number is 64, find the various other number.

Solution:

Given: GCF (y, 64) = 32 and LCM (y, 64) = 64∵ GCF × LCM = 64 × (y)⇒ y = (GCF × LCM)/64⇒ y = (32 × 64)/64⇒ y = 32Therefore, the various other number is 32.


Example 2: discover the best number the divides 64 and 32 exactly.

Solution:

The greatest number that divides 64 and 32 specifically is their greatest typical factor, i.e. GCF of 64 and 32.⇒ components of 64 and 32:

Factors that 64 = 1, 2, 4, 8, 16, 32, 64Factors that 32 = 1, 2, 4, 8, 16, 32

Therefore, the GCF that 64 and also 32 is 32.


Example 3: uncover the GCF the 64 and 32, if their LCM is 64.

Solution:

∵ LCM × GCF = 64 × 32⇒ GCF(64, 32) = (64 × 32)/64 = 32Therefore, the greatest common factor that 64 and 32 is 32.


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FAQs ~ above GCF of 64 and also 32

What is the GCF of 64 and 32?

The GCF of 64 and 32 is 32. To calculate the greatest common factor that 64 and also 32, we require to aspect each number (factors the 64 = 1, 2, 4, 8, 16, 32, 64; components of 32 = 1, 2, 4, 8, 16, 32) and also choose the greatest element that exactly divides both 64 and also 32, i.e., 32.

If the GCF the 32 and also 64 is 32, uncover its LCM.

GCF(32, 64) × LCM(32, 64) = 32 × 64Since the GCF the 32 and also 64 = 32⇒ 32 × LCM(32, 64) = 2048Therefore, LCM = 64☛ Greatest usual Factor Calculator

What is the Relation between LCM and GCF the 64, 32?

The following equation can be provided to express the relation between Least typical Multiple (LCM) and also GCF that 64 and 32, i.e. GCF × LCM = 64 × 32.

How to uncover the GCF that 64 and 32 through Long department Method?

To discover the GCF of 64, 32 using long division method, 64 is separated by 32. The equivalent divisor (32) when remainder amounts to 0 is taken as GCF.

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How to find the GCF the 64 and also 32 by prime Factorization?

To find the GCF that 64 and also 32, us will uncover the element factorization of the offered numbers, i.e. 64 = 2 × 2 × 2 × 2 × 2 × 2; 32 = 2 × 2 × 2 × 2 × 2.⇒ because 2, 2, 2, 2, 2 are typical terms in the prime factorization the 64 and also 32. Hence, GCF(64, 32) = 2 × 2 × 2 × 2 × 2 = 32☛ What space Prime Numbers?

What space the methods to discover GCF the 64 and 32?

There room three commonly used methods to find the GCF the 64 and 32.