GCF that 32 and 36 is the largest possible number that divides 32 and 36 precisely without any kind of remainder. The factors of 32 and 36 space 1, 2, 4, 8, 16, 32 and also 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There room 3 generally used techniques to discover the GCF that 32 and also 36 - Euclidean algorithm, lengthy division, and prime factorization.

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

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

Answer: GCF that 32 and 36 is 4.

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Explanation:

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


The techniques to discover the GCF of 32 and also 36 are described below.

Listing typical FactorsLong department MethodPrime factorization Method

GCF that 32 and 36 by Listing common Factors

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

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

GCF of 32 and 36 by long Division

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GCF that 32 and 36 is the divisor that we get when the remainder i do not care 0 after ~ doing long department repeatedly.

Step 2: due to the fact that the remainder ≠ 0, we will certainly divide the divisor of step 1 (32) by the remainder (4).Step 3: Repeat this process until the remainder = 0.

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

GCF that 32 and also 36 by prime Factorization

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Prime administrate of 32 and 36 is (2 × 2 × 2 × 2 × 2) and also (2 × 2 × 3 × 3) respectively. As 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 also 36 Examples


Example 1: discover the greatest number that divides 32 and also 36 exactly.

Solution:

The greatest number that divides 32 and 36 exactly is your greatest typical factor, i.e. GCF that 32 and also 36.⇒ components of 32 and also 36:

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

Therefore, the GCF that 32 and also 36 is 4.


Example 2: find the GCF that 32 and 36, if your LCM is 288.

Solution:

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


Example 3: For two numbers, GCF = 4 and also LCM = 288. If one number is 36, find 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 various other number is 32.


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FAQs top top GCF that 32 and also 36

What is the GCF of 32 and 36?

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

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

There space three commonly used methods to uncover the GCF the 32 and 36.

By lengthy DivisionBy element FactorizationBy Listing common Factors

How to discover the GCF of 32 and also 36 by Long division Method?

To uncover the GCF the 32, 36 utilizing long division method, 36 is divided by 32. The corresponding divisor (4) when remainder equates to 0 is taken together GCF.

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

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

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

The complying with equation deserve to be supplied to refer the relation between Least typical Multiple and also GCF the 32 and also 36, i.e. GCF × LCM = 32 × 36.

How to find the GCF that 32 and also 36 by prime Factorization?

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