Summarize this article:
125 LearnersLast updated on December 11, 2025
GCF of 189 and 200
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 189 and 200.
What is the GCF of 189 and 200?
The greatest common factor of 189 and 200 is 1.
The largest divisor of two or more numbers is called the GCF of the numbers.
If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.
The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 189 and 200?
To find the GCF of 189 and 200, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 189 and 200 by Using Listing of Factors
Steps to find the GCF of 189 and 200 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 189 = 1, 3, 7, 9, 21, 27, 63, 189. Factors of 200 = 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200.
Step 2: Now, identify the common factors of them Common factors of 189 and 200: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1.
The GCF of 189 and 200 is 1.
Explore Our Programs
GCF of 189 and 200 Using Prime Factorization
To find the GCF of 189 and 200 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 189: 189 = 3 × 3 × 3 × 7 = 3³ × 7 Prime Factors of 200: 200 = 2 × 2 × 2 × 5 × 5 = 2³ × 5²
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Multiply the common prime factors Since there are no common prime factors, the GCF is 1. The Greatest Common Factor of 189 and 200 is 1.
GCF of 189 and 200 Using Division Method or Euclidean Algorithm Method
Find the GCF of 189 and 200 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 200 by 189 200 ÷ 189 = 1 (quotient), The remainder is calculated as 200 − (189×1) = 11 The remainder is 11, not zero, so continue the process.
Step 2: Now divide the previous divisor (189) by the previous remainder (11) Divide 189 by 11 189 ÷ 11 = 17 (quotient), remainder = 189 − (11×17) = 2.
Step 3: Divide the previous divisor (11) by the previous remainder (2) 11 ÷ 2 = 5 (quotient), remainder = 11 − (2×5) = 1.
Step 4: Divide the previous divisor (2) by the previous remainder (1) 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 189 and 200 is 1.
Common Mistakes and How to Avoid Them in GCF of 189 and 200
Finding GCF of 189 and 200 looks simple, but students often make mistakes while calculating the GCF.
Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 189, students may mention 5 which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the wrong common factor
Students may sometimes select a factor that is not common or select an incorrect common factor.
To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers.
It is always important to include 1 as a factor, even if it doesn't affect the GCF in this case.
Mistake 4
Using Multiples instead of factors
Students confuse between factors and multiples.
In that confusion, sometimes they may write multiples instead of factors.
To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is always a non-zero value
Students may assume that GCF of two numbers will always be greater than zero.
However, if two numbers are co-prime, their GCF is 1.
To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 189 and 200 Examples
Problem 1
A gardener has 189 tulip bulbs and 200 daffodil bulbs. She wants to plant them in rows with an equal number of bulbs in each row, using the greatest number of bulbs possible. How many bulbs will be in each row?
We should find the GCF of 189 and 200 GCF of 189 and 200 is 1.
There is only 1 bulb in each row.
Explanation
As the GCF of 189 and 200 is 1, the gardener can only plant 1 bulb per row to ensure equal distribution.
Problem 2
A chef has 189 grams of flour and 200 grams of sugar. She wants to package them into the largest possible equal packets without any remaining. What should be the weight of each packet?
GCF of 189 and 200 is 1.
So each packet will weigh 1 gram.
Explanation
There are 189 grams of flour and 200 grams of sugar.
To find the total weight in each packet, we should find the GCF of 189 and 200.
There will be 1 gram in each packet.
Problem 3
An artist has 189 red beads and 200 blue beads. She wants to create necklaces with the same number of beads in each necklace, using the longest possible length. What should be the length of each necklace?
For calculating the longest equal length, we have to calculate the GCF of 189 and 200 The GCF of 189 and 200 is 1. Each necklace will be 1 bead long.
Explanation
For calculating the longest length of the necklace, first, we need to calculate the GCF of 189 and 200 which is 1.
Each necklace will be 1 bead long.
Problem 4
A builder has two wooden planks, one 189 cm long and the other 200 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The builder needs the longest piece of wood GCF of 189 and 200 is 1.
The longest length of each piece is 1 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 189 cm and 200 cm, respectively, we have to find the GCF of 189 and 200, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 189 and โaโ is 1, and the LCM is 37800. Find โaโ.
The value of ‘a’ is 200.
Explanation
GCF x LCM = product of the numbers
1 × 37800 = 189 × a
37800 = 189a
a = 37800 ÷ 189 = 200
FAQs on the Greatest Common Factor of 189 and 200
1.What is the LCM of 189 and 200?
2.Is 189 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 200?
5.Are 189 and 200 prime numbers?
Important Glossaries for GCF of 189 and 200
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 15 are 3 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 50 and 60 will be 10, as it is their largest common factor that divides the numbers completely.
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
