GCF of 7 and 16
2026-02-28 09:07 Diff
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Last updated on September 24, 2025

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 -

  1. Listing Factors
  2. Prime Factorization
  3. 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.

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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.

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 5

If the GCF of 7 and ‘b’ is 1, and the LCM is 112, find ‘b’.

Okay, lets begin

The value of ‘b’ is 16.

Explanation

GCF x LCM = product of the numbers

1 × 112 = 7 × b

112 = 7b

b = 112 ÷ 7 = 16

Well explained 👍

FAQs on the Greatest Common Factor of 7 and 16

1.What is the LCM of 7 and 16?

The LCM of 7 and 16 is 112.

2.Is 7 a prime number?

Yes, 7 is a prime number because it has only two factors: 1 and itself.

3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.

4.What is the prime factorization of 16?

The prime factorization of 16 is 2⁴.

5.Are 7 and 16 prime numbers?

No, 7 is a prime number, but 16 is not because 16 has more than two factors.

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.