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

You are watching: What is the gcf of 16 and 100

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

Answer: GCF that 16 and 100 is 4.

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Explanation:

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


The approaches to find the GCF that 16 and also 100 are explained below.

Listing typical FactorsPrime administrate MethodLong department Method

GCF that 16 and 100 through Listing usual Factors

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

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

GCF the 16 and also 100 by prime Factorization

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

GCF of 16 and also 100 by long Division

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

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

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

☛ likewise Check:


GCF that 16 and also 100 Examples


Example 1: The product of 2 numbers is 1600. If their GCF is 4, what is their 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 100 exactly.

Solution:

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

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

Therefore, the GCF the 16 and 100 is 4.


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

Solution:

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


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FAQs top top GCF the 16 and 100

What is the GCF of 16 and 100?

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

What are the techniques to find GCF the 16 and 100?

There room three generally used approaches to find the GCF of 16 and 100.

By Euclidean AlgorithmBy prime FactorizationBy long Division

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

The complying with equation deserve to be used to to express the relation in between LCM (Least common Multiple) and also GCF the 16 and also 100, i.e. GCF × LCM = 16 × 100.

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

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

How to uncover the GCF of 16 and also 100 by element Factorization?

To find the GCF the 16 and 100, us 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 common terms in the element factorization of 16 and 100. Hence, GCF(16, 100) = 2 × 2 = 4☛ What is a element Number?

How to discover the GCF the 16 and 100 through Long division Method?

To discover the GCF the 16, 100 making use of long department method, 100 is divided by 16. The equivalent divisor (4) once remainder equates to 0 is taken together GCF.