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, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 9 and 14.
The greatest common factor of 9 and 14 is 1. 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.
To find the GCF of 9 and 14, a few methods are described below -
Steps to find the GCF of 9 and 14 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 9 = 1, 3, 9.
Factors of 14 = 1, 2, 7, 14.
Step 2: Now, identify the common factors of them Common factors of 9 and 14: 1.
Step 3: Choose the largest factor
The largest factor that both numbers have is 1.
The GCF of 9 and 14 is 1.
To find the GCF of 9 and 14 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 9: 9 = 3 × 3 = 3²
Prime Factors of 14: 14 = 2 × 7
Step 2: Now, identify the common prime factors
There are no common prime factors.
Step 3: Since there are no common factors, the GCF is 1.
The Greatest Common Factor of 9 and 14 is 1.
Find the GCF of 9 and 14 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 14 by 9 14 ÷ 9 = 1 (quotient),
The remainder is calculated as 14 − (9×1) = 5
The remainder is 5, not zero, so continue the process
Step 2: Now divide the previous divisor (9) by the previous remainder (5)
Divide 9 by 5 9 ÷ 5 = 1 (quotient), remainder = 9 − (5×1) = 4
Step 3: Divide the previous divisor (5) by the remainder (4) 5 ÷ 4 = 1 (quotient), remainder = 5 − (4×1) = 1
Step 4: Divide the previous divisor (4) by the remainder (1) 4 ÷ 1 = 4 (quotient), remainder = 4 − (1×4) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 9 and 14 is 1.
Finding the GCF of 9 and 14 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A gardener has 9 rose bushes and 14 tulip plants. She wants to plant 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?
We should find the GCF of 9 and 14 GCF of 9 and 14
The GCF is 1.
There will be 1 plant in each row.
As the GCF of 9 and 14 is 1, the gardener can plant 1 plant per row.
A teacher has 9 notebooks and 14 markers. She wants to distribute them equally among students, with the largest number of items in each group. How many items will be in each group?
GCF of 9 and 14 The GCF is 1.
So each group will have 1 item.
There are 9 notebooks and 14 markers. To find the total number of items in each group, we should find the GCF of 9 and 14. There will be 1 item in each group.
A cook has 9 kg of potatoes and 14 kg of carrots. She wants to make soups with equal amounts of each, using the largest possible amount. What should be the amount of each ingredient in each soup?
For calculating equal amounts, we have to calculate the GCF of 9 and 14
The GCF is 1.
Each soup will have 1 kg of each ingredient.
For calculating the largest equal amount of ingredients, first, we need to calculate the GCF of 9 and 14, which is 1. Each soup will have 1 kg of potatoes and 1 kg of carrots.
A carpenter has two wooden planks, one 9 cm long and the other 14 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 9 and 14
The GCF is 1.
The longest length of each piece is 1 cm.
To find the longest length of each piece of the two wooden planks, 9 cm and 14 cm, respectively, we have to find the GCF of 9 and 14, which is 1 cm. The longest length of each piece is 1 cm.
If the GCF of 9 and ‘a’ is 3, and the LCM is 42, find ‘a’.
The value of ‘a’ is 14.
GCF × LCM = product of the numbers 3 × 42 = 9 × a
126 = 9a
a = 126 ÷ 9 = 14
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.