GCF that 16 and also 25 is the largest possible number that divides 16 and 25 precisely without any kind of remainder. The components of 16 and 25 are 1, 2, 4, 8, 16 and also 1, 5, 25 respectively. There room 3 commonly used approaches to uncover the GCF that 16 and also 25 - Euclidean algorithm, element factorization, and long division.

You are watching: What is the gcf of 16 and 25

1.GCF of 16 and 25
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 16 and 25 is 1.

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Explanation:

The GCF of 2 non-zero integers, x(16) and also y(25), is the greatest positive integer m(1) that divides both x(16) and y(25) without any kind of remainder.


Let's look in ~ the various methods for finding the GCF the 16 and also 25.

Long department MethodListing usual FactorsPrime factorization Method

GCF the 16 and 25 by long Division

GCF the 16 and also 25 is the divisor the we obtain when the remainder becomes 0 after ~ doing long division repeatedly.

Step 2: because the remainder ≠ 0, we will divide the divisor of action 1 (16) through the remainder (9).Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF the 16 and also 25.

GCF the 16 and also 25 by Listing usual Factors

Factors of 16: 1, 2, 4, 8, 16Factors that 25: 1, 5, 25

Since, 1 is the only typical factor between 16 and 25. The Greatest common Factor of 16 and also 25 is 1.

GCF of 16 and also 25 by prime Factorization

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Prime administrate of 16 and 25 is (2 × 2 × 2 × 2) and also (5 × 5) respectively. Together visible, there room no typical prime factors in between 16 and 25, i.e. They space co-prime. Hence, the GCF of 16 and 25 will be 1.

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GCF of 16 and 25 Examples


Example 1: The product of two numbers is 400. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and also product of numbers = 400∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 400/1Therefore, the LCM is 400.


Example 2: discover the GCF of 16 and 25, if their LCM is 400.

Solution:

∵ LCM × GCF = 16 × 25⇒ GCF(16, 25) = (16 × 25)/400 = 1Therefore, the greatest common factor that 16 and 25 is 1.


Example 3: find the biggest number that divides 16 and 25 exactly.

Solution:

The biggest number the divides 16 and also 25 exactly is their greatest typical factor, i.e. GCF the 16 and also 25.⇒ factors of 16 and also 25:

Factors the 16 = 1, 2, 4, 8, 16Factors that 25 = 1, 5, 25

Therefore, the GCF the 16 and 25 is 1.


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FAQs ~ above GCF that 16 and also 25

What is the GCF that 16 and also 25?

The GCF that 16 and 25 is 1. To calculate the GCF (Greatest common Factor) of 16 and 25, we need to aspect each number (factors the 16 = 1, 2, 4, 8, 16; determinants of 25 = 1, 5, 25) and also choose the greatest aspect that specifically divides both 16 and 25, i.e., 1.

If the GCF of 25 and 16 is 1, find its LCM.

GCF(25, 16) × LCM(25, 16) = 25 × 16Since the GCF that 25 and also 16 = 1⇒ 1 × LCM(25, 16) = 400Therefore, LCM = 400☛ Greatest usual Factor Calculator

What space the methods to discover GCF of 16 and also 25?

There are three typically used methods to discover the GCF that 16 and also 25.

By Euclidean AlgorithmBy element FactorizationBy long Division

What is the Relation between LCM and GCF the 16, 25?

The following equation deserve to be provided to express the relation in between LCM (Least typical Multiple) and also GCF that 16 and 25, i.e. GCF × LCM = 16 × 25.

See more: Catalytic Converters For 2000 Mercury Grand Marquis Catalytic Converter

How to find the GCF that 16 and also 25 through Long division Method?

To uncover the GCF that 16, 25 making use of long department method, 25 is split by 16. The matching divisor (1) once remainder amounts to 0 is taken as GCF.

How to uncover the GCF the 16 and 25 by prime Factorization?

To uncover the GCF the 16 and 25, we will find the element factorization of the offered numbers, i.e. 16 = 2 × 2 × 2 × 2; 25 = 5 × 5.⇒ over there is no usual prime factor for 16 and 25. Hence, GCF (16, 25) = 1.☛ element Numbers