GCF the 32 and also 36 is the largest feasible number that divides 32 and also 36 specifically without any kind of remainder. The determinants of 32 and also 36 space 1, 2, 4, 8, 16, 32 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There space 3 frequently used methods to find the GCF of 32 and also 36 - Euclidean algorithm, lengthy division, and prime factorization.

You are watching: Find the greatest common factor of 32 and 36

1.GCF that 32 and 36
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF of 32 and 36 is 4.

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Explanation:

The GCF of 2 non-zero integers, x(32) and also y(36), is the best positive integer m(4) that divides both x(32) and also y(36) without any type of remainder.


The methods to find the GCF the 32 and 36 are described below.

Listing typical FactorsLong department MethodPrime administer Method

GCF the 32 and 36 by Listing typical Factors

Factors of 32: 1, 2, 4, 8, 16, 32Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

There space 3 common factors of 32 and 36, that are 1, 2, and 4. Therefore, the greatest usual factor that 32 and also 36 is 4.

GCF the 32 and also 36 by lengthy Division

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GCF the 32 and also 36 is the divisor that we acquire when the remainder becomes 0 ~ doing long department repeatedly.

Step 2: since the remainder ≠ 0, we will certainly divide the divisor of step 1 (32) through the remainder (4).Step 3: Repeat this procedure until the remainder = 0.

The corresponding divisor (4) is the GCF the 32 and 36.

GCF of 32 and 36 by element Factorization

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Prime administrate of 32 and also 36 is (2 × 2 × 2 × 2 × 2) and (2 × 2 × 3 × 3) respectively. Together visible, 32 and 36 have usual prime factors. Hence, the GCF that 32 and also 36 is 2 × 2 = 4.

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GCF of 32 and 36 Examples


Example 1: find the biggest number the divides 32 and 36 exactly.

Solution:

The biggest number the divides 32 and 36 specifically is your greatest usual factor, i.e. GCF of 32 and 36.⇒ determinants of 32 and 36:

Factors of 32 = 1, 2, 4, 8, 16, 32Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36

Therefore, the GCF the 32 and 36 is 4.


Example 2: discover the GCF the 32 and 36, if their LCM is 288.

Solution:

∵ LCM × GCF = 32 × 36⇒ GCF(32, 36) = (32 × 36)/288 = 4Therefore, the greatest typical factor the 32 and also 36 is 4.


Example 3: For two numbers, GCF = 4 and also LCM = 288. If one number is 36, uncover the various other number.

Solution:

Given: GCF (y, 36) = 4 and LCM (y, 36) = 288∵ GCF × LCM = 36 × (y)⇒ y = (GCF × LCM)/36⇒ y = (4 × 288)/36⇒ y = 32Therefore, the other number is 32.


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FAQs on GCF of 32 and also 36

What is the GCF of 32 and 36?

The GCF the 32 and 36 is 4. To calculate the GCF the 32 and also 36, we require to factor each number (factors of 32 = 1, 2, 4, 8, 16, 32; determinants of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and also choose the greatest element that specifically divides both 32 and also 36, i.e., 4.

What are the approaches to find GCF that 32 and also 36?

There room three frequently used methods to discover the GCF that 32 and also 36.

By lengthy DivisionBy element FactorizationBy Listing common Factors

How to uncover the GCF that 32 and 36 by Long department Method?

To uncover the GCF of 32, 36 using long division method, 36 is separated by 32. The equivalent divisor (4) as soon as remainder equates to 0 is taken together GCF.

If the GCF the 36 and 32 is 4, discover its LCM.

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GCF(36, 32) × LCM(36, 32) = 36 × 32Since the GCF of 36 and also 32 = 4⇒ 4 × LCM(36, 32) = 1152Therefore, LCM = 288☛ Greatest usual Factor Calculator

What is the Relation between LCM and GCF that 32, 36?

The adhering to equation can be offered to refer the relation in between Least common Multiple and GCF the 32 and also 36, i.e. GCF × LCM = 32 × 36.

How to uncover the GCF of 32 and 36 by prime Factorization?

To discover the GCF that 32 and 36, us will uncover the prime factorization of the offered numbers, i.e. 32 = 2 × 2 × 2 × 2 × 2; 36 = 2 × 2 × 3 × 3.⇒ due to the fact that 2, 2 are common terms in the element factorization of 32 and 36. Hence, GCF(32, 36) = 2 × 2 = 4☛ What is a element Number?