Last updated on August 5th, 2025
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 30 and 5.
The greatest common factor of 30 and 5 is 5. 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.
To find the GCF of 30 and 5, a few methods are described below -
Steps to find the GCF of 30 and 5 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 5 = 1, 5.
Step 2: Now, identify the common factors of them Common factors of 30 and 5: 1, 5.
Step 3: Choose the largest factor
The largest factor that both numbers have is 5.
The GCF of 30 and 5 is 5.
To find the GCF of 30 and 5 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 5: 5 = 5
Step 2: Now, identify the common prime factors
The common prime factor is: 5
Step 3: Multiply the common prime factors
The Greatest Common Factor of 30 and 5 is 5.
Find the GCF of 30 and 5 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 30 by 5 30 ÷ 5 = 6 (quotient),
The remainder is calculated as 30 − (5×6) = 0
The remainder is zero, so the divisor will be the GCF.
The GCF of 30 and 5 is 5.
Finding GCF of 30 and 5 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A chef has 30 apples and 5 oranges. 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 5 GCF of 30 and 5 is 5.
There are 5 equal groups 30 ÷ 5 = 6 5 ÷ 5 = 1
There will be 5 groups, and each group gets 6 apples and 1 orange.
As the GCF of 30 and 5 is 5, the chef can make 5 groups. Now divide 30 and 5 by 5. Each group gets 6 apples and 1 orange.
A school has 30 red markers and 5 blue markers. They want to arrange them in rows with the same number of markers in each row, using the largest possible number of markers per row. How many markers will be in each row?
GCF of 30 and 5 is 5.
So each row will have 5 markers.
There are 30 red and 5 blue markers. To find the total number of markers in each row, we should find the GCF of 30 and 5. There will be 5 markers in each row.
A tailor has 30 meters of red fabric and 5 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 longest equal length, we have to calculate the GCF of 30 and 5
The GCF of 30 and 5 is 5.
The fabric is 5 meters long.
For calculating the longest length of the fabric, we first need to calculate the GCF of 30 and 5, which is 5. The length of each piece of fabric will be 5 meters.
A carpenter has two wooden planks, one 30 cm long and the other 5 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 5 is 5.
The longest length of each piece is 5 cm.
To find the longest length of each piece of the two wooden planks, 30 cm and 5 cm, respectively, we have to find the GCF of 30 and 5, which is 5 cm. The longest length of each piece is 5 cm.
If the GCF of 30 and ‘b’ is 5, and the LCM is 30. Find ‘b’.
The value of ‘b’ is 5.
GCF x LCM = product of the numbers 5 × 30 = 30 × b
150 = 30b
b = 150 ÷ 30 = 5
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.
: She loves to read number jokes and games.