GCF that 64 and also 32 is the largest feasible number that divides 64 and 32 specifically without any remainder. The determinants of 64 and also 32 space 1, 2, 4, 8, 16, 32, 64 and also 1, 2, 4, 8, 16, 32 respectively. There are 3 typically used approaches to find the GCF of 64 and also 32 - long division, prime factorization, and Euclidean algorithm.

You are watching: What is the gcf of 64 and 32

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

Answer: GCF of 64 and also 32 is 32.

*

Explanation:

The GCF of two non-zero integers, x(64) and y(32), is the greatest positive creature m(32) the divides both x(64) and also y(32) without any kind of remainder.


Let's look at the different methods because that finding the GCF the 64 and also 32.

Prime factorization MethodListing common FactorsLong division Method

GCF the 64 and also 32 by element Factorization

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

GCF of 64 and 32 by Listing usual Factors

*
Factors that 64: 1, 2, 4, 8, 16, 32, 64Factors of 32: 1, 2, 4, 8, 16, 32

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

GCF that 64 and also 32 by lengthy Division

GCF the 64 and 32 is the divisor that we acquire when the remainder becomes 0 ~ doing long department repeatedly.

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

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

☛ likewise Check:


GCF of 64 and also 32 Examples


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


Example 2: find the biggest number that divides 64 and also 32 exactly.

Solution:

The best number that divides 64 and 32 precisely is your greatest common factor, i.e. GCF of 64 and 32.⇒ factors of 64 and also 32:

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

Therefore, the GCF that 64 and 32 is 32.


Example 3: find the GCF of 64 and also 32, if your LCM is 64.

Solution:

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


Show equipment >

go to slidego to slidego to slide


*


Ready to view the people through math’s eyes?
Math is at the core of whatever we do. Enjoy solving real-world math troubles in live classes and also become an expert at everything.

Book a free Trial Class


FAQs ~ above GCF that 64 and also 32

What is the GCF that 64 and 32?

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

If the GCF the 32 and also 64 is 32, discover 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 typical Factor Calculator

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

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

How to discover the GCF of 64 and also 32 by Long division Method?

To uncover the GCF the 64, 32 making use of long division method, 64 is separated by 32. The corresponding divisor (32) when remainder amounts to 0 is taken together GCF.

See more: What Does Within 10 Days Mean By Within 7 Days? Prepositions

How to discover the GCF that 64 and 32 by element Factorization?

To find the GCF of 64 and 32, we will find the element factorization the the given numbers, i.e. 64 = 2 × 2 × 2 × 2 × 2 × 2; 32 = 2 × 2 × 2 × 2 × 2.⇒ due to the fact that 2, 2, 2, 2, 2 are usual terms in the element factorization the 64 and 32. Hence, GCF(64, 32) = 2 × 2 × 2 × 2 × 2 = 32☛ What space Prime Numbers?

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

There are three typically used methods to find the GCF of 64 and 32.