GCF of 14 and 16
2026-02-28 11:17 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, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 14 and 16.

What is the GCF of 14 and 16?

The greatest common factor of 14 and 16 is 2. 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 14 and 16?

To find the GCF of 14 and 16, a few methods are described below:

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

GCF of 14 and 16 by Using Listing of Factors

Steps to find the GCF of 14 and 16 using the listing of factors:

Step 1: Firstly, list the factors of each number

Factors of 14 = 1, 2, 7, 14.

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

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

Common factors of 14 and 16: 1, 2.

Step 3: Choose the largest factor:

The largest factor that both numbers have is 2.

The GCF of 14 and 16 is 2.

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GCF of 14 and 16 Using Prime Factorization

To find the GCF of 14 and 16 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 16: 16 = 2 x 2 x 2 x 2 = 24

Step 2: Now, identify the common prime factors.

The common prime factor is: 2

Step 3: Multiply the common prime factors 2.

The Greatest Common Factor of 14 and 16 is 2.

GCF of 14 and 16 Using Division Method or Euclidean Algorithm Method

Find the GCF of 14 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 14 16 ÷ 14 = 1 (quotient), The remainder is calculated as 16 - (14×1) = 2

The remainder is 2, not zero, so continue the process

Step 2: Now divide the previous divisor (14) by the previous remainder (2)

Divide 14 by 2 14 ÷ 2 = 7 (quotient), remainder = 14 - (2×7) = 0

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

The GCF of 14 and 16 is 2.

Common Mistakes and How to Avoid Them in GCF of 14 and 16

Finding GCF of 14 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

A gardener has 14 tulips and 16 roses. She wants to plant them in rows with the same number of flowers in each row. What is the largest number of flowers that can be in each row?

Okay, lets begin

We should find the GCF of 14 and 16.

The GCF of 14 and 16 is 2.

There will be 2 flowers in each row.

Explanation

As the GCF of 14 and 16 is 2, the gardener can plant 2 flowers per row.

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Problem 2

A farmer has 14 apple trees and 16 orange trees. He wants to arrange them in the largest possible equal rows. How many trees will be in each row?

Okay, lets begin

GCF of 14 and 16 is 2. So each row will have 2 trees.

Explanation

There are 14 apple and 16 orange trees.

To find the total number of trees in each row, we should find the GCF of 14 and 16.

There will be 2 trees in each row.

Well explained 👍

Problem 3

A baker has 14 loaves of sourdough bread and 16 loaves of rye bread. She wants to package them in boxes with the same number of loaves, using the largest possible number of loaves per box. How many loaves should be in each box?

Okay, lets begin

For calculating the largest equal number of loaves, we have to calculate the GCF of 14 and 16.

The GCF of 14 and 16 is 2.

Each box will contain 2 loaves.

Explanation

For calculating the largest number of loaves per box, first, we need to calculate the GCF of 14 and 16, which is 2. The number of loaves in each box will be 2.

Well explained 👍

Problem 4

A student has two pieces of ribbon, one 14 cm long and the other 16 cm long. He wants to cut them into the longest possible equal pieces, without any ribbon left over. What should be the length of each piece?

Okay, lets begin

The student needs the longest piece of ribbon.

GCF of 14 and 16 is 2.

The length of each piece is 2 cm.

Explanation

To find the longest length of each piece of the two ribbons, 14 cm and 16 cm respectively, we have to find the GCF of 14 and 16, which is 2 cm.

The longest length of each piece is 2 cm.

Well explained 👍

Problem 5

If the GCF of 14 and ‘b’ is 2, and the LCM is 112, find ‘b’.

Okay, lets begin

The value of ‘b’ is 16.

Explanation

GCF x LCM = product of the numbers

2 × 112 = 14 × b

224 = 14b

b = 224 ÷ 14 = 16

Well explained 👍

FAQs on the Greatest Common Factor of 14 and 16

1.What is the LCM of 14 and 16?

The LCM of 14 and 16 is 112.

2.Is 14 divisible by 2?

Yes, 14 is divisible by 2 because it is an even number.

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 2^4.

5.Are 14 and 16 prime numbers?

No, 14 and 16 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 14 and 16

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, 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 10 are 2 and 5.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 14 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.