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102 LearnersLast updated on September 24, 2025
GCF of 7 and 16
The GCF (Greatest Common Factor) 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 7 and 16.
What is the GCF of 7 and 16?
The greatest common factor of 7 and 16 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.
How to find the GCF of 7 and 16?
To find the GCF of 7 and 16, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 7 and 16 by Using Listing of Factors
Steps to find the GCF of 7 and 16 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 7 = 1, 7.
Factors of 16 = 1, 2, 4, 8, 16.
Step 2: Now, identify the common factors of them Common factors of 7 and 16: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 7 and 16 is 1.
GCF of 7 and 16 Using Prime Factorization
To find the GCF of 7 and 16 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 7: 7 is a prime number, so its only prime factor is 7.
Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 2⁴
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Since there are no common prime factors, the GCF is 1. The Greatest Common Factor of 7 and 16 is 1.
GCF of 7 and 16 Using Division Method or Euclidean Algorithm Method
Find the GCF of 7 and 16 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 16 by 7 16 ÷ 7 = 2 (quotient), The remainder is calculated as 16 − (7×2) = 2 The remainder is 2, not zero, so continue the process
Step 2: Now divide the previous divisor (7) by the previous remainder (2) Divide 7 by 2 7 ÷ 2 = 3 (quotient), remainder = 7 − (2×3) = 1 The remainder is 1, not zero, so continue the process
Step 3: Now divide the previous divisor (2) by the previous remainder (1) Divide 2 by 1 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 7 and 16 is 1.
Common Mistakes and How to Avoid Them in GCF of 7 and 16
Finding the GCF of 7 and 16 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 16, students may mention 3, 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 recognizing there is only one common factor, 1. To avoid this confusion, students should list all the common factors properly and find the greatest one, which in this case is 1.
Mistake 3
Forgetting that the GCF of co-prime numbers is 1
Sometimes students may forget that if two numbers are co-prime, their GCF is 1. Remembering that co-prime numbers have no common factors other than 1 will help avoid this mistake.
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 greater than 1 for all pairs of numbers
Students may assume that the GCF of two numbers will always be greater than 1. But for co-prime numbers, the GCF is 1. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 7 and 16 Examples
Problem 1
An artist has two canvases, one 7 inches tall and the other 16 inches tall. She wants to divide them into equal sections of the largest possible size. What should be the size of each section?
We should find the GCF of 7 and 16 The GCF of 7 and 16 is 1. Each section will be 1 inch.
Explanation
As the GCF of 7 and 16 is 1, the artist can divide the canvases into sections of 1 inch.
Problem 2
A gardener has two pieces of land, one measuring 7 meters and the other 16 meters. He wants to create plots of equal size using the largest possible measurement. How large should each plot be?
The GCF of 7 and 16 is 1. So each plot will be 1 meter.
Explanation
There are pieces of land measuring 7 meters and 16 meters. To find the largest plot size, we should find the GCF of 7 and 16, which is 1 meter.
Problem 3
A baker has 7 kilograms of wheat flour and 16 kilograms of sugar. She wants to package them in bags of equal weight, using the largest possible weight for each bag. What should be the weight of each bag?
For calculating the largest equal weight, we have to calculate the GCF of 7 and 16 The GCF of 7 and 16 is 1. Each bag will weigh 1 kilogram.
Explanation
For calculating the largest weight of the bags, first we need to calculate the GCF of 7 and 16, which is 1. The weight of each bag will be 1 kilogram.
Problem 4
A carpenter has two wooden beams, one 7 feet long and the other 16 feet long. He wants to cut them into the longest possible equal pieces without any leftover wood. What should be the length of each piece?
The carpenter needs the longest piece of wood The GCF of 7 and 16 is 1.
The longest length of each piece is 1 foot.
Explanation
To find the longest length of each piece of the two wooden beams, 7 feet and 16 feet, respectively, we have to find the GCF of 7 and 16, which is 1 foot. The longest length of each piece is 1 foot.
Problem 5
If the GCF of 7 and ‘b’ is 1, and the LCM is 112, find ‘b’.
The value of ‘b’ is 16.
Explanation
GCF x LCM = product of the numbers
1 × 112 = 7 × b
112 = 7b
b = 112 ÷ 7 = 16
FAQs on the Greatest Common Factor of 7 and 16
1.What is the LCM of 7 and 16?
2.Is 7 a prime number?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 16?
5.Are 7 and 16 prime numbers?
Important Glossaries for GCF of 7 and 16
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.
- 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 factor of 7 is 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 16 is divided by 7, the remainder is 2 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 7 and 16 is 112.
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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.
