GCF of 5 and 16
2026-02-28 17:11 Diff
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Last updated on August 5, 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 5 and 16.

What is the GCF of 5 and 16?

The greatest common factor of 5 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, meaning they have no common factors other than 1, their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.

How to find the GCF of 5 and 16?

To find the GCF of 5 and 16, a few methods are described below:

  • Listing Factors
  • Prime Factorization
  • Long Division Method / by Euclidean Algorithm

GCF of 5 and 16 by Using Listing of Factors

Steps to find the GCF of 5 and 16 using the listing of factors:

Step 1: Firstly, list the factors of each number.

Factors of 5 = 1, 5.

Factors of 16 = 1, 2, 4, 8, 16.

Step 2: Now, identify the common factors of them.

Common factor of 5 and 16: 1.

Step 3: Choose the largest factor.

The largest factor that both numbers have is 1.

The GCF of 5 and 16 is 1.

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GCF of 5 and 16 Using Prime Factorization

To find the GCF of 5 and 16 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number.

Prime Factors of 5: 5 = 5

Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 2^4

Step 2: Now, identify the common prime factors.

There are no common prime factors other than 1

Step 3: Since there's no shared prime factor, the GCF is 1.

GCF of 5 and 16 Using Division Method or Euclidean Algorithm Method

Find the GCF of 5 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 5. 16 ÷ 5 = 3 (quotient),

The remainder is calculated as 16 − (5×3) = 1.

The remainder is 1, not zero, so continue the process.

Step 2: Now divide the previous divisor (5) by the previous remainder (1).

Divide 5 by 1. 5 ÷ 1 = 5 (quotient), remainder = 5 − (1×5) = 0.

The remainder is zero, the divisor will become the GCF.

The GCF of 5 and 16 is 1.

Common Mistakes and How to Avoid Them in GCF of 5 and 16

Finding the GCF of 5 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

There are 5 apples and 16 oranges. A vendor wants to pack them into baskets with the same number of fruits in each basket. How many fruits will be in each basket?

Okay, lets begin

We should find the GCF of 5 and 16.

The GCF of 5 and 16 is 1.

Thus, there will be 1 fruit per basket, making a total of 21 baskets.

Explanation

As the GCF of 5 and 16 is 1, the vendor can make 21 baskets, each containing 1 fruit.

Well explained 👍

Problem 2

A gardener has 5 rose plants and 16 tulip plants. She wants to plant them in rows with the same number of plants in each row. How many plants will be in each row?

Okay, lets begin

The GCF of 5 and 16 is 1.

So each row will have 1 plant.

Explanation

There are 5 rose and 16 tulip plants. To find the total number of plants in each row, we should find the GCF of 5 and 16. There will be 1 plant in each row.

Well explained 👍

Problem 3

A baker has 5 chocolate cakes and 16 vanilla cakes. She wants to cut both types of cakes into equal pieces, using the longest possible length. What should be the length of each piece?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 5 and 16

The GCF of 5 and 16 is 1.

Each piece will be equivalent to 1 unit of the cake.

Explanation

For calculating the longest length of the cake pieces, first we need to calculate the GCF of 5 and 16, which is 1. The length of each piece of the cake will be 1 unit.

Well explained 👍

Problem 4

A tailor has two pieces of fabric, one 5 meters long and the other 16 meters long. He wants to cut them into the longest possible equal pieces, without any fabric left over. What should be the length of each piece?

Okay, lets begin

The tailor needs the longest piece of fabric.

The GCF of 5 and 16 is 1.

The longest length of each piece is 1 meter.

Explanation

To find the longest length of each piece of the two fabrics, 5 meters and 16 meters, respectively, we have to find the GCF of 5 and 16, which is 1 meter. The longest length of each piece is 1 meter.

Well explained 👍

Problem 5

If the GCF of 5 and ‘a’ is 1, and the LCM is 80, find ‘a’.

Okay, lets begin

The value of ‘a’ is 16.

Explanation

GCF x LCM = product of the numbers 1 × 80 = 5 × a

80 = 5a

a = 80 ÷ 5 = 16

Well explained 👍

FAQs on the Greatest Common Factor of 5 and 16

1.What is the LCM of 5 and 16?

The LCM of 5 and 16 is 80.

2.Is 5 divisible by 2?

No, 5 is not divisible by 2 because it is an odd number.

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

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

4.What is the prime factorization of 16?

The prime factorization of 16 is 2^4.

5.Are 5 and 16 prime numbers?

5 is a prime number because it has only two factors, 1 and itself. 16 is not a prime number because it has more than two factors.

Important Glossaries for GCF of 5 and 16

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 5 are 1 and 5.
  • Co-prime numbers: Two numbers that have no common factors other than 1. For example, 5 and 16 are co-prime.
  • 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 5 is 5.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 16 is divided by 5, the remainder is 1.
  • LCM: The smallest common multiple of two or more numbers is termed the LCM. For example, the LCM of 5 and 16 is 80.

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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.