GCF of 14 and 10
2026-02-28 13:27 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 the items equally, to group or arrange items and schedule events. In this topic, we will learn about the GCF of 14 and 10.

What is the GCF of 14 and 10?

The greatest common factor of 14 and 10 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 10?

To find the GCF of 14 and 10, a few methods are described below -

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

GCF of 14 and 10 by Using Listing of Factors

Steps to find the GCF of 14 and 10 using the listing of factors

Step 1: Firstly, list the factors of each number

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

Factors of 10 = 1, 2, 5, 10.

Step 2: Now, identify the common factors of them Common factors of 14 and 10: 1, 2.

Step 3: Choose the largest factor

The largest factor that both numbers have is 2.

The GCF of 14 and 10 is 2.

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GCF of 14 and 10 Using Prime Factorization

To find the GCF of 14 and 10 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 10: 10 = 2 x 5

Step 2: Now, identify the common prime factors

The common prime factor is: 2

Step 3: Multiply the common prime factors

The GCF of 14 and 10 is 2.

GCF of 14 and 10 Using Division Method or Euclidean Algorithm Method

Find the GCF of 14 and 10 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number

Here, divide 14 by 10 14 ÷ 10 = 1 (quotient)

The remainder is calculated as 14 − (10×1) = 4

The remainder is 4, not zero, so continue the process

Step 2: Now divide the previous divisor (10) by the previous remainder (4)

Divide 10 by 4 10 ÷ 4 = 2 (quotient), remainder = 10 − (4×2) = 2

The remainder is not zero, so continue

Step 3: Divide the previous divisor (4) by the previous remainder (2)

Divide 4 by 2 4 ÷ 2 = 2 (quotient), remainder = 4 − (2×2) = 0

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

The GCF of 14 and 10 is 2.

Common Mistakes and How to Avoid Them in GCF of 14 and 10

Finding the GCF of 14 and 10 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 baker has 14 chocolate muffins and 10 blueberry muffins. She wants to arrange them into equal sets with the largest number of muffins in each set. How many muffins will be in each set?

Okay, lets begin

We should find the GCF of 14 and 10 GCF of 14 and 10 is 2.

There are 2 muffins in each set. 14 ÷ 2 = 7

10 ÷ 2 = 5

There will be 2 muffins in each set, with 7 sets of chocolate muffins and 5 sets of blueberry muffins.

Explanation

As the GCF of 14 and 10 is 2, the baker can make sets with 2 muffins each. Now divide 14 and 10 by 2. Each set has 7 chocolate muffins and 5 blueberry muffins.

Well explained 👍

Problem 2

A gardener has 14 apple trees and 10 orange trees. He wants to plant them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?

Okay, lets begin

GCF of 14 and 10 is 2.

So each row will have 2 trees.

Explanation

There are 14 apple trees and 10 orange trees. To find the total number of trees in each row, we should find the GCF of 14 and 10. There will be 2 trees in each row.

Well explained 👍

Problem 3

A chef has 14 kilograms of flour and 10 kilograms of sugar. She wants to divide both into containers of equal weight, with the largest possible weight. What should be the weight of each container?

Okay, lets begin

For calculating the largest equal weight, we have to calculate the GCF of 14 and 10

The GCF of 14 and 10 is 2.

Each container should weigh 2 kilograms.

Explanation

For calculating the largest weight of the containers, first we need to calculate the GCF of 14 and 10 which is 2. Each container will weigh 2 kilograms.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 14 cm long and the other 10 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 GCF of 14 and 10 is 2.

The longest length of each piece is 2 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 14 cm and 10 cm, respectively. We have to find the GCF of 14 and 10, which is 2 cm. The longest length of each piece is 2 cm.

Well explained 👍

Problem 5

If the GCF of 14 and ‘a’ is 2, and the LCM is 70. Find ‘a’.

Okay, lets begin

The value of ‘a’ is 10.

Explanation

GCF x LCM = product of the numbers 2 × 70 = 14 × a

140 = 14a

a = 140 ÷ 14 = 10

Well explained 👍

FAQs on the Greatest Common Factor of 14 and 10

1.What is the LCM of 14 and 10?

The LCM of 14 and 10 is 70.

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 10?

The prime factorization of 10 is 2 × 5.

5.Are 14 and 10 prime numbers?

No, 14 and 10 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 14 and 10

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
  • 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, 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 14 are 2 and 7.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 4, the remainder is 2 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 10 is 70.

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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.