Gcf Of 16 And 25

How to find the Greatest Common Gene of xvi and 25?

In that location are many methods we can apply to summate the GCF of 16 and 25.

In our first method, we'll observe out the prime factorisation of the 16 and 25 numbers.

In our second method, nosotros'll create a listing of all the factors of the xvi and 25 numbers.

These are the numbers that divide the sixteen and 25 numbers without a residuum.

Once we have these, all we have to do is to find the ane that is the biggest common number from the two lists.

At present allow'southward look at each methods, and calculate the GCF of 16 and 25.

• Prime Factorisation
• Listing of factors
• Euclidean algorithm
• Binary Greatest Common Divisor algorithm

Method 1 - Prime Factorisation

With the prime factorisation method, all we accept to practice is to find the common prime factors of 16 and 25, and then multiply them. Really uncomplicated:

Step ane: Let's create a list of all the prime factors of 16 and 25:

Prime factors of 16:

As you lot tin can see beneath, the prime factors of sixteen are 2, 2, 2 and 2.

Let's illustrate the prime factorization of xvi in exponential form:

xvi = two^four

Prime factors of 25:

Equally you lot can see beneath, the prime factors of 25 are 5 and 5.

Let's illustrate the prime number factorization of 25 in exponential grade:

25 = v²

Step two: Write down a list of all the common prime factors of xvi and 25:

As seen in the boxes above, the common prime factors of 16 and 25 are 1.

Step 3: All we have to practice now is to multiply these common prime factors:

Notice the production of all mutual prime number factors by multiplying them:

1^one=i

Done!

According to our calculations above, the Greatest Common Factor of 16 and 25 is 1

Method 2 - List of Factors

With this simple method, we'll need to find all the factors of 16 and 25, factors are numbers that carve up the another number without a residue, and merely identify the mutual ones, then cull which is the largest one.

Step one: Create a list of all the numbers that carve up 16 and 25 without a remainder:

List of factors that dissever 16 without a rest are:

1, ii, 8 and 16.

List of factors that dissever 25 without a remainder are:

1 and 25.

Step 2: Place the largest common number from the 2 lists higher up:

As you tin see in the lists of factors from to a higher place, for the numbers 16 and 25, we have highlighted the number i, which ways that we have found the Greatest Common Gene, or GCF.

According to our calculations above, the Greatest Common Gene of xvi and 25 is i

Method 3 - Euclidean algorithm

The Euclidean algorithm says that if number k is the GCM of xvi and 25, so the number thou is as well the GCM of the division residuum of the numbers 16 and 25.

We follow this procedure until the reminder is 0.

The Greatest Mutual Divisor is the final nonzero number.

Step i: Sort the numbers into ascending lodge:

16, 25

Footstep 2

Accept out, from the set, the smallers number as you divisor: 16

The remaining set is: 25

Notice the reminder of the division betwixt the number and the divisor

25 mod 16 = ix

Gather the divisor and all of the remainders and sort them in ascending club. Remove any duplicates and 0. Our set is:

9, 16

Repeat the process until there is merely one number in the gear up.

Take out, from the set, the smallers number as you divisor: 9

The remaining set is: 16

Discover the reminder of the division between the number and the divisor

16 mod 9 = seven

Assemble the divisor and all of the remainders and sort them in ascending order. Remove whatsoever duplicates and 0. Our set is:

7, 9

Repeat the process until there is just one number in the set.

Take out, from the fix, the smallers number equally you divisor: 7

The remaining gear up is: nine

Find the reminder of the division between the number and the divisor

9 mod seven = two

Get together the divisor and all of the remainders and sort them in ascending order. Remove any duplicates and 0. Our set is:

2, seven

Repeat the process until there is only one number in the ready.

Take out, from the prepare, the smallers number as you lot divisor: two

The remaining fix is: vii

Find the reminder of the division between the number and the divisor

7 modernistic two = 1

Gather the divisor and all of the remainders and sort them in ascending order. Remove whatsoever duplicates and 0. Our set up is:

1, 2

Repeat the process until at that place is only one number in the set.

Take out, from the set, the smallers number as you lot divisor: one

The remaining set is: 2

Find the reminder of the division between the number and the divisor

two modern 1 = 0

Gather the divisor and all of the remainders and sort them in ascending order. Remove whatever duplicates and 0. Our set is:

ane

Step iii: Take the remaining number from our set

The Greatest Common Factor of 16 and 25 is 1

Method 4 - Binary Greatest Common Divisor algorithm

The binary GCD algorithm, also known as Stein'due south algorithm or the binary Euclidean algorithm, is an algorithm that computes the greatest common divisor of two nonnegative integers. Stein's algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm; it replaces partitioning with arithmetic shifts, comparisons, and subtraction.

Although the algorithm in its contemporary form was kickoff published by the Israeli physicist and developer Josef Stein in 1967, it may have been known by the 2nd century BCE, in ancient People's republic of china.

Footstep 1: Sort the numbers, and set initial GCF equal to 1

The list: 16, 25

Step 2: Divide all of the remaining fifty-fifty values by 2, remove the duplicates and sort.
Repeat the process if there are fifty-fifty numbers in the listing:

16/ii = eight

The resulting listing: viii, 25

viii/two = 4

The resulting list: four, 25

4/ii = 2

The resulting listing: ii, 25

2/2 = ane

The resulting list: 1, 25

Step iii: Pick the offset number, one.
Subtract 1 from the remaining value(due south) and split the upshot by 2.
Remove the duplicates and sort:

(25-1)/2 = 12

The resulting listing: i, 12

Step 4: Carve up all of the remaining even values by 2, remove the duplicates and sort.
Repeat the procedure if there are even numbers in the listing:

12/2 = 6

The resulting listing: 1, 6

half dozen/2 = iii

The resulting listing: 1, 3

Footstep 5: Pick the outset number, 1.
Subtract ane from the remaining value(south) and divide the outcome past 2.
Remove the duplicates and sort:

(3-1)/2 = 1

The resulting list: 1

Step 6: Only one number remains, 1.
Multiply it past your current GCF:

GCF = i*1 = 1

The Greatest Common Factor of 16 and 25 is one

Gcf Of 16 And 25,

Source: https://www.gcf-lcm.com/gcf-of-16-25/

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