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102 LearnersLast updated on September 10, 2025
GCF of 30 and 100
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 30 and 100.
What is the GCF of 30 and 100?
The greatest common factor of 30 and 100 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 30 and 100?
To find the GCF of 30 and 100, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / Euclidean Algorithm
GCF of 30 and 100 by Using Listing of Factors
Steps to find the GCF of 30 and 100 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100.
Step 2: Now, identify the common factors of them Common factors of 30 and 100: 1, 2, 5, 10.
Step 3: Choose the largest factor The largest factor that both numbers have is 10. The GCF of 30 and 100 is 10.
GCF of 30 and 100 Using Prime Factorization
To find the GCF of 30 and 100 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 30: 30 = 2 x 3 x 5
Prime Factors of 100: 100 = 2 x 2 x 5 x 5
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 30 and 100 is 10.
GCF of 30 and 100 Using Division Method or Euclidean Algorithm Method
Find the GCF of 30 and 100 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 100 by 30 100 ÷ 30 = 3 (quotient), The remainder is calculated as 100 − (30×3) = 10 The remainder is 10, not zero, so continue the process
Step 2: Now divide the previous divisor (30) by the previous remainder (10) Divide 30 by 10 30 ÷ 10 = 3 (quotient), remainder = 30 − (10×3) = 0
The remainder is zero, so the divisor becomes the GCF. The GCF of 30 and 100 is 10.
Common Mistakes and How to Avoid Them in GCF of 30 and 100
Finding the GCF of 30 and 100 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 30, 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 indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse 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 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 30 and 100 Examples
Problem 1
A painter has 30 brushes and 100 paint tubes. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 30 and 100. GCF of 30 and 100 is 10.
There are 10 equal groups. 30 ÷ 10 = 3 100 ÷ 10 = 10
There will be 10 groups, and each group gets 3 brushes and 10 paint tubes.
Explanation
As the GCF of 30 and 100 is 10, the painter can make 10 groups. Now divide 30 and 100 by 10. Each group gets 3 brushes and 10 paint tubes.
Problem 2
A garden has 30 rose bushes and 100 tulip plants. They want to arrange them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
GCF of 30 and 100 The GCF is 10. So each row will have 10 plants.
Explanation
There are 30 rose bushes and 100 tulip plants. To find the total number of plants in each row, we should find the GCF of 30 and 100. There will be 10 plants in each row.
Problem 3
A tailor has 30 meters of silk ribbon and 100 meters of cotton ribbon. She wants to cut both ribbons 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 30 and 100. The GCF of 30 and 100 is 10. The ribbon pieces are 10 meters long.
Explanation
For calculating the longest length of the ribbon, first we need to calculate the GCF of 30 and 100, which is 10. The length of each piece of the ribbon will be 10 meters.
Problem 4
A carpenter has two wooden planks, one 30 cm long and the other 100 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 30 and 100 is 10. The longest length of each piece is 10 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 30 cm and 100 cm, respectively, we have to find the GCF of 30 and 100, which is 10 cm. The longest length of each piece is 10 cm.
Problem 5
If the GCF of 30 and ‘b’ is 10, and the LCM is 300. Find ‘b’.
The value of ‘b’ is 100.
Explanation
GCF x LCM = product of the numbers
10 × 300 = 30 × b
3000 = 30b
b = 3000 ÷ 30 = 100
FAQs on the Greatest Common Factor of 30 and 100
1.What is the LCM of 30 and 100?
2.Is 30 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 100?
5.Are 30 and 100 prime numbers?
Important Glossaries for GCF of 30 and 100
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 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 30 are 2, 3, and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 100 is divided by 30, the remainder is 10, and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 30 and 100 is 300.
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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.
