GCF that 16 and 100 is the largest possible number that divides 16 and also 100 precisely without any remainder. The factors of 16 and also 100 room 1, 2, 4, 8, 16 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There space 3 generally used methods to discover the GCF of 16 and also 100 - element factorization, Euclidean algorithm, and also long division.

You are watching: What is the greatest common factor of 16

1.GCF that 16 and 100
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF that 16 and also 100 is 4.

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Explanation:

The GCF of 2 non-zero integers, x(16) and y(100), is the greatest positive integer m(4) that divides both x(16) and also y(100) without any kind of remainder.


The methods to discover the GCF the 16 and also 100 are explained below.

Listing common FactorsPrime factorization MethodLong department Method

GCF that 16 and 100 through Listing common Factors

Factors of 16: 1, 2, 4, 8, 16Factors the 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

There are 3 typical factors the 16 and 100, that are 1, 2, and also 4. Therefore, the greatest typical factor of 16 and 100 is 4.

GCF that 16 and also 100 by prime Factorization

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Prime factorization of 16 and 100 is (2 × 2 × 2 × 2) and also (2 × 2 × 5 × 5) respectively. As visible, 16 and also 100 have typical prime factors. Hence, the GCF the 16 and also 100 is 2 × 2 = 4.

GCF that 16 and 100 by long Division

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GCF of 16 and also 100 is the divisor that we gain when the remainder becomes 0 after ~ doing long division repeatedly.

Step 2: since the remainder ≠ 0, we will certainly divide the divisor of action 1 (16) by the remainder (4).Step 3: Repeat this process until the remainder = 0.

The equivalent divisor (4) is the GCF of 16 and 100.

☛ additionally Check:


GCF that 16 and 100 Examples


Example 1: The product of 2 numbers is 1600. If your GCF is 4, what is your LCM?

Solution:

Given: GCF = 4 and product of numbers = 1600∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 1600/4Therefore, the LCM is 400.


Example 2: find the greatest number the divides 16 and also 100 exactly.

Solution:

The biggest number that divides 16 and also 100 specifically is your greatest usual factor, i.e. GCF of 16 and 100.⇒ components of 16 and also 100:

Factors that 16 = 1, 2, 4, 8, 16Factors that 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100

Therefore, the GCF that 16 and 100 is 4.


Example 3: discover the GCF the 16 and also 100, if your LCM is 400.

Solution:

∵ LCM × GCF = 16 × 100⇒ GCF(16, 100) = (16 × 100)/400 = 4Therefore, the greatest usual factor that 16 and 100 is 4.


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FAQs ~ above GCF that 16 and also 100

What is the GCF of 16 and also 100?

The GCF the 16 and 100 is 4. To calculate the GCF that 16 and 100, we require to factor each number (factors of 16 = 1, 2, 4, 8, 16; components of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the greatest element that precisely divides both 16 and also 100, i.e., 4.

What space the techniques to discover GCF the 16 and also 100?

There are three frequently used methods to uncover the GCF of 16 and also 100.

By Euclidean AlgorithmBy element FactorizationBy long Division

What is the Relation in between LCM and also GCF that 16, 100?

The adhering to equation can be provided to to express the relation in between LCM (Least typical Multiple) and also GCF that 16 and 100, i.e. GCF × LCM = 16 × 100.

If the GCF the 100 and 16 is 4, find its LCM.

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GCF(100, 16) × LCM(100, 16) = 100 × 16Since the GCF that 100 and 16 = 4⇒ 4 × LCM(100, 16) = 1600Therefore, LCM = 400☛ GCF Calculator

How to discover the GCF of 16 and 100 by prime Factorization?

To find the GCF that 16 and also 100, we will find the element factorization that the provided numbers, i.e. 16 = 2 × 2 × 2 × 2; 100 = 2 × 2 × 5 × 5.⇒ because 2, 2 are typical terms in the element factorization that 16 and also 100. Hence, GCF(16, 100) = 2 × 2 = 4☛ What is a prime Number?

How to uncover the GCF that 16 and 100 by Long division Method?

To uncover the GCF of 16, 100 using long department method, 100 is separated by 16. The equivalent divisor (4) when remainder amounts to 0 is taken together GCF.