To change these 189 and 200 numbers, you re welcome amend the worths in the areas below:

## How to find the Greatest common Factor that 189 and also 200?

There are numerous methods we can use to calculate the GCF that 189 and 200.

You are watching: What is the greatest common factor of 189 and 200

In our very first method, we"ll discover out the prime factorisation that the 189 and 200 numbers.

In our 2nd method, we"ll produce a list of every the components of the 189 and 200 numbers.

These room the number that division the 189 and also 200 numbers there is no a remainder.

Once we have actually these, all we need to do is to discover the one the is the biggest usual number indigenous the 2 lists.

Now let"s watch at every methods, and calculate the GCF the 189 and 200.

Methods of calculating the GCF the 189 and 200:### Method 1 - prime Factorisation

With the prime factorisation method, every we need to do is to discover the typical prime determinants of 189 and 200, and also then main point them. Yes, really simple:

Step 1: Let"s produce a list of all the prime determinants of 189 and also 200:Prime components of 189:

As you can see below, the prime determinants of 189 are **3, 3, 3 and also 7**.

Let"s show the prime factorization the **189** in exponential form:

**189** = 33x71

Prime components of 200:

As you have the right to see below, the prime components of **200** room **2, 2, 2, 5 and 5**.

Let"s show the element factorization that **200** in exponential form:

**200** = 23x52

**Step 2: compose down a list of every the typical prime components of 189 and also 200:**

**As checked out in the boxes above, the common prime factors of 189 and also 200 are 1**.**Step 3: every we need to do now is to multiply these usual prime factors:Find the product the all common prime determinants by multiply them:**

**11=1**

According to our calculations above, the **Greatest common Factor** of 189 and 200 is **1**

### Method 2 - list of Factors

With this simple method, we"ll need to discover all the determinants of 189 and also 200,factors room numbers that division the an additional number without a remainder, and also simply identify the usual ones, then pick which is the biggest one.

**Step 1: create a perform of all the number that division 189 and 200 there is no a remainder:**

**List of components that division 189** without a remainder are:

**1, 3, 7, 9, 21, 27, 63 and also 189**.

List of determinants that division **200** without a remainder are:

**1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and also 200**.

**Step 2: determine the largest typical number from the 2 lists above:**

As you can see in the lists of determinants from above, because that the number 189 and also 200, we have highlighted the number **1**, which method that us have discovered the Greatest common Factor, or GCF.

According to our calculations above, the **Greatest usual Factor that **189 and 200 is **1**

### Method 3 - Euclidean algorithm

**The Euclidean algorithm claims that if number k** is the GCM that 189 and 200,then the number **k** is also the GCM that the department remainder the the number 189 and also 200.

We monitor this procedure until the reminder is 0.

The Greatest common Divisor is the critical nonzero number.

**Step 1: type the numbers into ascending order:**

189, 200

Step 2

**Take out, indigenous the set, the smallers number as you divisor: 189**

The remaining set is: 200

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

200 mode 189 = 11

**Gather the divisor and every one of the remainders and also sort lock in ascending order.Remove any kind of duplicates and 0. Our collection is:**

11, 189

Repeat the procedure until over there is just one number in the set.

**Take out, native the set, the smallers number together you divisor: 11**

The remaining set is: 189

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

189 mode 11 = 2

**Gather the divisor and all of the remainders and also sort them in ascending order.Remove any duplicates and 0. Our collection is:**

2, 11

Repeat the procedure until over there is only one number in the set.

**Take out, indigenous the set, the smallers number together you divisor: 2**

The remaining collection is: 11

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

11 mode 2 = 1

**Gather the divisor and all of the remainders and sort lock in ascending order.Remove any kind of duplicates and 0. Our set is:**

1, 2

Repeat the procedure until over there is just one number in the set.

**Take out, from the set, the smallers number together you divisor: 1**

The remaining collection is: 2

Find the reminder that the department between the number and the divisor

2 mod 1 = 0

Gather the divisor and all of the remainders and also sort lock in ascending order.Remove any kind of duplicates and 0. Our set is:1

Step 3: take the staying number from our set

The **Greatest common Factor of **189 and also 200 is **1**

### Method 4 - Binary Greatest common Divisor algorithm

The binary GCD algorithm, additionally known together Stein"s algorithm or the binary Euclidean algorithm, is one algorithm that computes the greatest usual divisor of two nonnegative integers. Stein"s algorithm uses much easier arithmetic operations than the traditional Euclidean algorithm; that replaces division with arithmetic shifts, comparisons, and subtraction.

See more: What Is The Answer To Question 72 On The Impossible Quiz Answers Levels 71

return the algorithm in its contemporary form was very first published by the Israeli physicist and also programmer Josef Stein in 1967, that may have actually been well-known by the second century BCE, in old China.

Step 1: type the numbers, and collection initial GCF same to 1The list: 189, 200

Step 2: Divide all of the remaining also values by 2, eliminate the duplicates and also sort.Repeat the procedure if there are even numbers in the list:

200/2 = 100

The result list: 100, 189

100/2 = 50

The result list: 50, 189

50/2 = 25

The resulting list: 25, 189

Step 3: pick the first number, 25.Subtract 25 native the continuing to be value(s) and divide the outcome by 2.Remove the duplicates and sort:

(189-25)/2 = 82

The resulting list: 25, 82

Step 4: Divide all of the remaining even values by 2, eliminate the duplicates and also sort.Repeat the procedure if there are even numbers in the list:

82/2 = 41

The resulting list: 25, 41

Step 5: pick the first number, 25.Subtract 25 from the continuing to be value(s) and divide the outcome by 2.Remove the duplicates and sort:

(41-25)/2 = 8

The result list: 8, 25

Step 6: Divide every one of the remaining also values by 2, eliminate the duplicates and sort.Repeat the procedure if there are also numbers in the list:

8/2 = 4

The resulting list: 4, 25

4/2 = 2

The resulting list: 2, 25

2/2 = 1

The result list: 1, 25

Step 7: pick the very first number, 1.Subtract 1 from the staying value(s) and divide the outcome by 2.Remove the duplicates and sort:

(25-1)/2 = 12

The resulting list: 1, 12

Step 8: Divide all of the remaining also values by 2, remove the duplicates and sort.Repeat the process if over there are also numbers in the list:

12/2 = 6

The result list: 1, 6

6/2 = 3

The result list: 1, 3

Step 9: pick the an initial number, 1.Subtract 1 from the staying value(s) and divide the result by 2.Remove the duplicates and also sort:

(3-1)/2 = 1

The result list: 1

Step 10: only one number remains, 1.Multiply that by your current GCF:

GCF = 1*1 = 1