GCF of 16 and 19
2026-02-28 19:04 Diff
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Last updated on September 20, 2025

The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 16 and 19.

What is the GCF of 16 and 19?

The greatest common factor of 16 and 19 is 1. 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 16 and 19?

To find the GCF of 16 and 19, a few methods are described below 

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

GCF of 16 and 19 by Using Listing of Factors

Steps to find the GCF of 16 and 19 using the listing of factors

Step 1: Firstly, list the factors of each number

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

Factors of 19 = 1, 19.

Step 2: Now, identify the common factors of them Common factor of 16 and 19: 1.

Step 3: Choose the largest factor The largest factor that both numbers have is 1.

The GCF of 16 and 19 is 1.

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GCF of 16 and 19 Using Prime Factorization

To find the GCF of 16 and 19 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number

Prime Factors of 16: 16 = 2 × 2 × 2 × 2 = 24

Prime Factors of 19: 19 is a prime number, so its only prime factor is 19.

Step 2: Now, identify the common prime factors There are no common prime factors.

Step 3: The GCF is the product of the lowest power of all common prime factors. Since there are no common prime factors, the GCF is 1.

The Greatest Common Factor of 16 and 19 is 1.

GCF of 16 and 19 Using Division Method or Euclidean Algorithm Method

Find the GCF of 16 and 19 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 19 by 16 19 ÷ 16 = 1 (quotient),

The remainder is calculated as 19 − (16×1) = 3

The remainder is 3, not zero, so continue the process

Step 2: Now divide the previous divisor (16) by the previous remainder (3)

Divide 16 by 3 16 ÷ 3 = 5 (quotient), remainder = 16 − (3×5) = 1

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

Step 3: Now divide the previous divisor (3) by the previous remainder (1)

Divide 3 by 1 3 ÷ 1 = 3 (quotient), remainder = 3 − (1×3) = 0

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

The GCF of 16 and 19 is 1.

Common Mistakes and How to Avoid Them in GCF of 16 and 19

Finding the GCF of 16 and 19 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.

Problem 1

A teacher has 16 apples and 19 oranges. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?

Okay, lets begin

We should find the GCF of 16 and 19.

The GCF of 16 and 19 is 1.

There are 1 equal group. 16 ÷ 1 = 16 19 ÷ 1 = 19

There will be 1 group, and each group gets 16 apples and 19 oranges.

Explanation

As the GCF of 16 and 19 is 1, the teacher can make one group.

Now divide 16 and 19 by 1.

Each group gets all 16 apples and 19 oranges.

Well explained 👍

Problem 2

A school has 16 red chairs and 19 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?

Okay, lets begin

The GCF of 16 and 19 is 1. So each row will have 1 chair.

Explanation

There are 16 red and 19 blue chairs.

To find the total number of chairs in each row, we should find the GCF of 16 and 19.

Each row will have 1 chair.

Well explained 👍

Problem 3

A tailor has 16 meters of red ribbon and 19 meters of blue 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?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 16 and 19.

The GCF of 16 and 19 is 1.

Each piece of ribbon will be 1 meter long.

Explanation

For calculating the longest length of the ribbon, first, we need to calculate the GCF of 16 and 19, which is 1.

The length of each piece of ribbon will be 1 meter.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 16 cm long and the other 19 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?

Okay, lets begin

The carpenter needs the longest piece of wood. The GCF of 16 and 19 is 1. The longest length of each piece is 1 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 16 cm and 19 cm, respectively, we have to find the GCF of 16 and 19, which is 1 cm.

The longest length of each piece is 1 cm.

Well explained 👍

Problem 5

If the GCF of 16 and ‘b’ is 1, and the LCM is 304, find ‘b’.

Okay, lets begin

The value of ‘b’ is 19.

Explanation

GCF × LCM = product of the numbers

1 × 304 = 16 × b

304 = 16b

b = 304 ÷ 16 = 19

Well explained 👍

FAQs on the Greatest Common Factor of 16 and 19

1.What is the LCM of 16 and 19?

The LCM of 16 and 19 is 304.

2.Is 16 divisible by 4?

Yes, 16 is divisible by 4 because 16 ÷ 4 = 4, leaving no remainder.

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 the GCF of any two co-prime numbers.

4.What is the prime factorization of 19?

The prime factorization of 19 is 19, as it is a prime number.

5.Are 16 and 19 prime numbers?

No, 16 is not a prime number because it has more than two factors. However, 19 is a prime number as it has only two factors: 1 and 19.

Important Glossaries for GCF of 16 and 19

  • Factors: Factors are numbers that divide a target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.
  • Co-prime Numbers: Two numbers are co-prime if their GCF is 1. For example, 16 and 19 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 factors of 16 are all 2s.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 16 and 19 is 304.
  • Remainder: The value left after division when a number cannot be divided evenly. For example, when 19 is divided by 16, the remainder is 3.

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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.