Summarize this article:
104 LearnersLast updated on September 11, 2025
GCF of 14 and 63
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 14 and 63.
What is the GCF of 14 and 63?
The greatest common factor of 14 and 63 is 7. 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 14 and 63?
To find the GCF of 14 and 63, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 14 and 63 by Using Listing of Factors
Steps to find the GCF of 14 and 63 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 14 = 1, 2, 7, 14. Factors of 63 = 1, 3, 7, 9, 21, 63.
Step 2: Now, identify the common factors of them Common factors of 14 and 63: 1, 7.
Step 3: Choose the largest factor The largest factor that both numbers have is 7. The GCF of 14 and 63 is 7.
GCF of 14 and 63 Using Prime Factorization
To find the GCF of 14 and 63 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 14: 14 = 2 x 7
Prime Factors of 63: 63 = 3 x 3 x 7 = 3² x 7
Step 2: Now, identify the common prime factors The common prime factor is: 7
Step 3: Multiply the common prime factors 7 = 7
The Greatest Common Factor of 14 and 63 is 7.
GCF of 14 and 63 Using Division Method or Euclidean Algorithm Method
Find the GCF of 14 and 63 using the Division Method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 63 by 14 63 ÷ 14 = 4 (quotient) The remainder is calculated as 63 − (14 x 4) = 7
The remainder is 7, not zero, so continue the process
Step 2: Now divide the previous divisor (14) by the previous remainder (7) Divide 14 by 7 14 ÷ 7 = 2 (quotient), remainder = 14 − (7 x 2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 14 and 63 is 7.
Common Mistakes and How to Avoid Them in GCF of 14 and 63
Finding the GCF of 14 and 63 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors. For example, while listing factors of 14, students may mention 10 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 14 and 63 Examples
Problem 1
A gardener has 14 rose plants and 63 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 14 and 63 GCF of 14 and 63 is 7.
There are 7 equal groups. 14 ÷ 7 = 2 63 ÷ 7 = 9
There will be 7 groups, and each group gets 2 rose plants and 9 tulip plants.
Explanation
As the GCF of 14 and 63 is 7, the gardener can make 7 groups. Now divide 14 and 63 by 7. Each group gets 2 rose plants and 9 tulip plants.
Problem 2
A baker has 14 chocolate bars and 63 cookies. They want to package them in boxes, with the same number of each item in each box, using the largest possible number of items per box. How many items will be in each box?
GCF of 14 and 63 is 7.
So each box will have 7 items.
Explanation
There are 14 chocolate bars and 63 cookies. To find the total number of items in each box, we should find the GCF of 14 and 63. There will be 7 items in each box.
Problem 3
A tailor has 14 meters of silk ribbon and 63 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 14 and 63.
The GCF of 14 and 63 is 7. The ribbon is 7 meters long.
Explanation
For calculating the longest length of the ribbon, first we need to calculate the GCF of 14 and 63, which is 7. The length of each piece of the ribbon will be 7 meters.
Problem 4
A carpenter has two wooden planks, one 14 cm long and the other 63 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 14 and 63 is 7. The longest length of each piece is 7 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 14 cm and 63 cm, respectively, we have to find the GCF of 14 and 63, which is 7 cm. The longest length of each piece is 7 cm.
Problem 5
If the GCF of 14 and ‘b’ is 7, and the LCM is 126, find ‘b’.
The value of ‘b’ is 63.
Explanation
GCF x LCM = product of the numbers
7 x 126 = 14 x b
882 = 14b
b = 882 ÷ 14 = 63
FAQs on the Greatest Common Factor of 14 and 63
1.What is the LCM of 14 and 63?
2.Is 14 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 63?
5.Are 14 and 63 prime numbers?
Important Glossaries for GCF of 14 and 63
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 7 are 1 and 7.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, 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 14 are 2 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 5, the remainder is 4 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 14 and 63 is 126.
Explore More numbers
![Important Math Links Icon]()
Previous to GCF of 14 and 63
![Important Math Links Icon]()
Next to GCF of 14 and 63
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.
