GCF the 12 and also 32 is the largest possible number that divides 12 and 32 precisely without any type of remainder. The determinants of 12 and 32 room 1, 2, 3, 4, 6, 12 and 1, 2, 4, 8, 16, 32 respectively. There space 3 generally used techniques to discover the GCF the 12 and also 32 - prime factorization, Euclidean algorithm, and also long division.

You are watching: Common factors of 12 and 32

1.GCF that 12 and 32
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF the 12 and also 32 is 4.

*

Explanation:

The GCF of two non-zero integers, x(12) and also y(32), is the biggest positive creature m(4) that divides both x(12) and also y(32) without any remainder.


Let's look in ~ the various methods because that finding the GCF the 12 and 32.

Long division MethodListing typical FactorsPrime factorization Method

GCF that 12 and 32 by lengthy Division

GCF the 12 and also 32 is the divisor the we gain when the remainder becomes 0 after ~ doing long department repeatedly.

Step 2: due to the fact that the remainder ≠ 0, we will certainly divide the divisor of action 1 (12) through the remainder (8).Step 3: Repeat this process until the remainder = 0.

The equivalent divisor (4) is the GCF the 12 and also 32.

GCF of 12 and 32 by Listing common Factors

*
Factors that 12: 1, 2, 3, 4, 6, 12Factors of 32: 1, 2, 4, 8, 16, 32

There room 3 typical factors of 12 and 32, that room 1, 2, and 4. Therefore, the greatest usual factor the 12 and 32 is 4.

GCF that 12 and also 32 by prime Factorization

*

Prime administrate of 12 and 32 is (2 × 2 × 3) and (2 × 2 × 2 × 2 × 2) respectively. Together visible, 12 and also 32 have usual prime factors. Hence, the GCF the 12 and 32 is 2 × 2 = 4.

☛ also Check:


GCF of 12 and also 32 Examples


Example 1: The product of two numbers is 384. If your GCF is 4, what is your LCM?

Solution:

Given: GCF = 4 and product of number = 384∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 384/4Therefore, the LCM is 96.


Example 2: find the greatest number the divides 12 and also 32 exactly.

Solution:

The best number the divides 12 and 32 exactly is your greatest typical factor, i.e. GCF that 12 and also 32.⇒ factors of 12 and also 32:

Factors that 12 = 1, 2, 3, 4, 6, 12Factors the 32 = 1, 2, 4, 8, 16, 32

Therefore, the GCF the 12 and 32 is 4.


Example 3: uncover the GCF the 12 and 32, if your LCM is 96.

Solution:

∵ LCM × GCF = 12 × 32⇒ GCF(12, 32) = (12 × 32)/96 = 4Therefore, the greatest common factor of 12 and also 32 is 4.


Show equipment >

go to slidego come slidego to slide


*


Ready to view the civilization through math’s eyes?
Math is at the main point of whatever we do. Enjoy solving real-world math troubles in live classes and become an skilled at everything.

Book a totally free Trial Class


FAQs top top GCF the 12 and 32

What is the GCF that 12 and 32?

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

What space the approaches to find GCF the 12 and also 32?

There space three typically used approaches to find the GCF that 12 and also 32.

By Euclidean AlgorithmBy element FactorizationBy lengthy Division

How to uncover the GCF that 12 and 32 through Long department Method?

To discover the GCF of 12, 32 using long department method, 32 is separated by 12. The matching divisor (4) as soon as remainder equates to 0 is taken together GCF.

How to discover the GCF of 12 and 32 by element Factorization?

To find the GCF that 12 and 32, we will uncover the element factorization the the provided numbers, i.e. 12 = 2 × 2 × 3; 32 = 2 × 2 × 2 × 2 × 2.⇒ because 2, 2 are common terms in the element factorization of 12 and 32. Hence, GCF(12, 32) = 2 × 2 = 4☛ What are Prime Numbers?

What is the Relation in between LCM and GCF that 12, 32?

The adhering to equation can be supplied to refer the relation in between Least common Multiple (LCM) and also GCF of 12 and also 32, i.e. GCF × LCM = 12 × 32.

See more: Where Is The Armory In Vault 34 Armory?: Fnv Where Is The Armory In Vault 34

If the GCF the 32 and also 12 is 4, find its LCM.

GCF(32, 12) × LCM(32, 12) = 32 × 12Since the GCF the 32 and also 12 = 4⇒ 4 × LCM(32, 12) = 384Therefore, LCM = 96☛ GCF Calculator