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104 LearnersLast updated on September 24, 2025
GCF of 180 and 1750
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items and schedule events. In this topic, we will learn about the GCF of 180 and 1750.
What is the GCF of 180 and 1750?
The greatest common factor of 180 and 1750 is 10.
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 180 and 1750?
To find the GCF of 180 and 1750, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 180 and 1750 by Using Listing of Factors
Steps to find the GCF of 180 and 1750 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 30, 36, 45, 60, 90, 180.
Factors of 1750 = 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, 1750.
Step 2: Now, identify the common factors of them Common factors of 180 and 1750: 1, 2, 5, 10.
Step 3: Choose the largest factor The largest factor that both numbers have is 10.
The GCF of 180 and 1750 is 10.
GCF of 180 and 1750 Using Prime Factorization
To find the GCF of 180 and 1750 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 180: 180 = 2 x 2 x 3 x 3 x 5 = 2² x 3² x 5
Prime Factors of 1750: 1750 = 2 x 5 x 5 x 5 x 7 = 2 x 5³ x 7
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 5
Step 3: Multiply the common prime factors 2 x 5 = 10.
The Greatest Common Factor of 180 and 1750 is 10.
GCF of 180 and 1750 Using Division Method or Euclidean Algorithm Method
Find the GCF of 180 and 1750 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 1750 by 180 1750 ÷ 180 = 9 (quotient), The remainder is calculated as 1750 − (180×9) = 70 The remainder is 70, not zero, so continue the process
Step 2: Now divide the previous divisor (180) by the previous remainder (70) Divide 180 by 70 180 ÷ 70 = 2 (quotient), remainder = 180 − (70×2) = 40 Continue the process
Step 3: Divide the previous divisor (70) by the previous remainder (40) 70 ÷ 40 = 1 (quotient), remainder = 70 − (40×1) = 30
Step 4: Divide the previous divisor (40) by the previous remainder (30) 40 ÷ 30 = 1 (quotient), remainder = 40 − (30×1) = 10
Step 5: Divide the previous divisor (30) by the previous remainder (10) 30 ÷ 10 = 3 (quotient), remainder = 30 − (10×3) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 180 and 1750 is 10.
Common Mistakes and How to Avoid Them in GCF of 180 and 1750
Finding GCF of 180 and 1750 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 180, students may mention 8 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 the smallest common factor instead of the largest one. 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. However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
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 an even number
Students may assume that GCF of two numbers will always be an even number. But it's not true that a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 180 and 1750 Examples
Problem 1
A baker has 180 cupcakes and 1750 cookies. He wants to package them into the largest possible number of identical boxes, with the same number of cupcakes and cookies in each box. How many items will be in each box?
We should find GCF of 180 and 1750 GCF of 180 and 1750 2 x 5 = 10.
There are 10 equal groups 180 ÷ 10 = 18 1750 ÷ 10 = 175
There will be 10 boxes, and each box gets 18 cupcakes and 175 cookies.
Explanation
As the GCF of 180 and 1750 is 10, the baker can make 10 boxes.
Now divide 180 and 1750 by 10.
Each box gets 18 cupcakes and 175 cookies.
Problem 2
A concert organizer has 180 seats in one section and 1750 seats in another section. He wants to arrange them in rows with the same number of seats in each row, using the largest possible number of seats per row. How many seats will be in each row?
GCF of 180 and 1750 2 x 5 = 10.
So each row will have 10 seats.
Explanation
There are 180 seats and 1750 seats in different sections.
To find the total number of seats in each row, we should find the GCF of 180 and 1750.
There will be 10 seats in each row.
Problem 3
A tailor has 180 meters of silk and 1750 meters of cotton. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 180 and 1750 The GCF of 180 and 1750 2 x 5 = 10.
The fabric is 10 meters long.
Explanation
For calculating the longest length of the fabric first, we need to calculate the GCF of 180 and 1750, which is 10.
The length of each piece of the fabric will be 10 meters.
Problem 4
A carpenter has two wooden planks, one 180 cm long and the other 1750 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 carpenter needs the longest piece of wood GCF of 180 and 1750 2 x 5 = 10.
The longest length of each piece is 10 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 180 cm and 1750 cm, respectively.
We have to find the GCF of 180 and 1750, which is 10 cm.
The longest length of each piece is 10 cm.
Problem 5
If the GCF of 180 and ‘b’ is 10, and the LCM is 3150. Find ‘b’.
The value of ‘b’ is 175.
Explanation
GCF x LCM = product of the numbers
10 × 3150 = 180 × b
31500 = 180b
b = 31500 ÷ 180 = 175
FAQs on the Greatest Common Factor of 180 and 1750
1.What is the LCM of 180 and 1750?
2.Is 180 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 1750?
5.Are 180 and 1750 prime numbers?
Important Glossaries for GCF of 180 and 1750
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- Prime Factorization: Prime Factorization is the process of expressing a number as a product of its prime factors. For example, the prime factorization of 18 is 2 x 3².
- Greatest Common Factor (GCF): The largest factor that commonly divides two or more numbers. For example, the GCF of 100 and 150 is 50.
- Euclidean Algorithm: A method to find the GCF of two numbers based on the division process. It involves repeated division and remainders.
- Least Common Multiple (LCM): The smallest common multiple of two or more numbers. For example, the LCM of 12 and 15 is 60.
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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.
