101 LearnersLast updated on August 12, 2025
GCF of 30 and 70
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 to schedule events. In this topic, we will learn about the GCF of 30 and 70.
What is the GCF of 30 and 70?
The greatest common factor of 30 and 70 is 10. 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 30 and 70?
To find the GCF of 30 and 70, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 30 and 70 by Using Listing of Factors
Steps to find the GCF of 30 and 70 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 70 = 1, 2, 5, 7, 10, 14, 35, 70.
Step 2: Now, identify the common factors of them Common factors of 30 and 70: 1, 2, 5, 10.
Step 3: Choose the largest factor The largest factor that both numbers have is 10. The GCF of 30 and 70 is 10.
GCF of 30 and 70 Using Prime Factorization
To find the GCF of 30 and 70 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 30: 30 = 2 × 3 × 5 Prime Factors of 70: 70 = 2 × 5 × 7
Step 2: Now, identify the common prime factors The common prime factors are: 2 × 5
Step 3: Multiply the common prime factors 2 × 5 = 10. The Greatest Common Factor of 30 and 70 is 10.
GCF of 30 and 70 Using Division Method or Euclidean Algorithm Method
Find the GCF of 30 and 70 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 70 by 30 70 ÷ 30 = 2 (quotient), The remainder is calculated as 70 − (30×2) = 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, the divisor will become the GCF. The GCF of 30 and 70 is 10.
Common Mistakes and How to Avoid Them in GCF of 30 and 70
Finding the GCF of 30 and 70 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 70 Examples
Problem 1
A gardener has 30 rose bushes and 70 sunflower plants. She wants to plant them in rows with an equal number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
We should find the GCF of 30 and 70 GCF of 30 and 70 2×5 = 10. There are 10 equal rows 30 ÷ 10 = 3 70 ÷ 10 = 7 There will be 10 rows, and each row gets 3 rose bushes and 7 sunflower plants.
Explanation
As the GCF of 30 and 70 is 10, the gardener can make 10 rows. Now divide 30 and 70 by 10. Each row gets 3 rose bushes and 7 sunflower plants.
Problem 2
A bakery has 30 chocolate cupcakes and 70 vanilla cupcakes. They want to arrange them in boxes with the same number of cupcakes in each box, using the largest possible number of cupcakes per box. How many cupcakes will be in each box?
GCF of 30 and 70 2×5 = 10. So each box will have 10 cupcakes.
Explanation
There are 30 chocolate and 70 vanilla cupcakes. To find the total number of cupcakes in each box, we should find the GCF of 30 and 70. There will be 10 cupcakes in each box.
Problem 3
A designer has 30 meters of red fabric and 70 meters of blue 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 30 and 70 The GCF of 30 and 70 2×5 = 10. The fabric is 10 meters long.
Explanation
For calculating the longest length of the fabric, first we need to calculate the GCF of 30 and 70, which is 10. The length of each piece of the fabric will be 10 meters.
Problem 4
A carpenter has two wooden planks, one 30 cm long and the other 70 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 70 2×5 = 10. The longest length of each piece is 10 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 30 cm and 70 cm, respectively, we have to find the GCF of 30 and 70, which is 10 cm. The longest length of each piece is 10 cm.
Problem 5
If the GCF of 30 and ‘a’ is 10, and the LCM is 210. Find ‘a’.
The value of ‘a’ is 70.
Explanation
GCF × LCM = product of the numbers
10 × 210 = 30 × a
2100 = 30a
a = 2100 ÷ 30 = 70
FAQs on the Greatest Common Factor of 30 and 70
1.What is the LCM of 30 and 70?
2.Is 30 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 70?
5.Are 30 and 70 prime numbers?
6.How can children in Philippines use numbers in everyday life to understand GCF of 30 and 70?
7.What are some fun ways kids in Philippines can practice GCF of 30 and 70 with numbers?
8.What role do numbers and GCF of 30 and 70 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve GCF of 30 and 70 skills?
Important Glossaries for GCF of 30 and 70
- 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 30 is divided by 7, the remainder is 2, and the quotient is 4.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 30 and 70 is 210.
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.
