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106 LearnersLast updated on September 24, 2025
GCF of 360 and 150
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 to schedule events. In this topic, we will learn about the GCF of 360 and 150.
What is the GCF of 360 and 150?
The greatest common factor of 360 and 150 is 30. The largest divisor of two or more numbers is called the GCF of the number.
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 360 and 150?
To find the GCF of 360 and 150, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 360 and 150 by Using Listing of Factors
Steps to find the GCF of 360 and 150 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 360 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. Factors of 150 = 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150.
Step 2: Now, identify the common factors of them Common factors of 360 and 150: 1, 2, 3, 5, 6, 10, 15, 30.
Step 3: Choose the largest factor The largest factor that both numbers have is 30. The GCF of 360 and 150 is 30.
GCF of 360 and 150 Using Prime Factorization
To find the GCF of 360 and 150 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 360: 360 = 2 x 2 x 2 x 3 x 3 x 5 = 2³ x 3² x 5 Prime Factors of 150: 150 = 2 x 3 x 5 x 5 = 2 x 3 x 5²
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 3 x 5
Step 3: Multiply the common prime factors 2 x 3 x 5 = 30.
The Greatest Common Factor of 360 and 150 is 30.
GCF of 360 and 150 Using Division Method or Euclidean Algorithm Method
Find the GCF of 360 and 150 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 360 by 150 360 ÷ 150 = 2 (quotient), The remainder is calculated as 360 − (150 x 2) = 60 The remainder is 60, not zero, so continue the process
Step 2: Now divide the previous divisor (150) by the previous remainder (60) Divide 150 by 60 150 ÷ 60 = 2 (quotient), remainder = 150 − (60 x 2) = 30
Step 3: Now divide 60 by 30 60 ÷ 30 = 2 (quotient), remainder = 60 − (30 x 2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 360 and 150 is 30.
Common Mistakes and How to Avoid Them in GCF of 360 and 150
Finding the GCF of 360 and 150 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 360, students may mention 7, 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 indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse factors with 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 the GCF of two numbers will always be an even number. But it's not true; 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 360 and 150 Examples
Problem 1
A chef has 360 grams of flour and 150 grams of sugar. He wants to divide them into equal portions with the largest possible mass in each portion. How much will each portion weigh?
We should find the GCF of 360 and 150 GCF of 360 and 150 2 x 3 x 5 = 30. There are 30 equal portions 360 ÷ 30 = 12 150 ÷ 30 = 5 There will be 30 portions, and each portion will have 12 grams of flour and 5 grams of sugar.
Explanation
As the GCF of 360 and 150 is 30, the chef can make 30 portions.
Now divide 360 and 150 by 30.
Each portion will have 12 grams of flour and 5 grams of sugar.
Problem 2
A gardener has 360 tulip bulbs and 150 daffodil bulbs. He wants to plant them in rows with the same number of bulbs in each row, using the largest possible number of bulbs per row. How many bulbs will be in each row?
GCF of 360 and 150 2 x 3 x 5 = 30. So each row will have 30 bulbs.
Explanation
To find the total number of bulbs in each row, we should find the GCF of 360 and 150.
There will be 30 bulbs in each row.
Problem 3
A tailor has 360 meters of blue fabric and 150 meters of red fabric. 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 360 and 150 The GCF of 360 and 150 2 x 3 x 5 = 30. The fabric pieces will be 30 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 360 and 150, which is 30.
The length of each piece of fabric will be 30 meters.
Problem 4
A carpenter has two wooden planks, one 360 cm long and the other 150 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 360 and 150 2 x 3 x 5 = 30. The longest length of each piece is 30 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 360 cm and 150 cm, respectively, we have to find the GCF of 360 and 150, which is 30 cm.
The longest length of each piece is 30 cm.
Problem 5
If the GCF of 360 and ‘b’ is 30, and the LCM is 1800, find ‘b’.
The value of ‘b’ is 150.
Explanation
GCF x LCM = product of the numbers
30 × 1800 = 360 × b
54000 = 360b
b = 54000 ÷ 360
= 150
FAQs on the Greatest Common Factor of 360 and 150
1.What is the LCM of 360 and 150?
2.Is 360 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 150?
5.Are 360 and 150 prime numbers?
Important Glossaries for GCF of 360 and 150
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
- 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 360 are 2, 3, and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 17 is divided by 5, the remainder is 2 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 360 and 150 is 1800.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 360 and 150 is 30, as it is their largest common factor that divides the numbers completely.
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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.
