GCF of 51 and 3
2026-02-28 11:44 Diff
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Last updated on September 9, 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 to schedule events. In this topic, we will learn about the GCF of 51 and 3.

What is the GCF of 51 and 3?

The greatest common factor of 51 and 3 is 3. 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 51 and 3?

To find the GCF of 51 and 3, a few methods are described below 

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

GCF of 51 and 3 by Using Listing of Factors

Steps to find the GCF of 51 and 3 using the listing of factors:

Step 1: Firstly, list the factors of each number Factors of 51 = 1, 3, 17, 51. Factors of 3 = 1, 3.

Step 2: Now, identify the common factors of them Common factors of 51 and 3: 1, 3.

Step 3: Choose the largest factor The largest factor that both numbers have is 3. The GCF of 51 and 3 is 3.

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GCF of 51 and 3 Using Prime Factorization

To find the GCF of 51 and 3 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number Prime Factors of 51: 51 = 3 x 17 Prime Factors of 3: 3 = 3

Step 2: Now, identify the common prime factors The common prime factor is: 3

Step 3: Multiply the common prime factors 3 = 3. The Greatest Common Factor of 51 and 3 is 3.

GCF of 51 and 3 Using Division Method or Euclidean Algorithm Method

Find the GCF of 51 and 3 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 51 by 3 51 ÷ 3 = 17 (quotient), The remainder is 51 − (3×17) = 0 The remainder is zero, so the divisor will become the GCF. The GCF of 51 and 3 is 3.

Common Mistakes and How to Avoid Them in GCF of 51 and 3

Finding the GCF of 51 and 3 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 51 markers and 3 boards. 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 51 and 3. GCF of 51 and 3 is 3. There are 3 equal groups 51 ÷ 3 = 17 3 ÷ 3 = 1 There will be 3 groups, and each group gets 17 markers and 1 board.

Explanation

As the GCF of 51 and 3 is 3, the teacher can make 3 groups.

Now divide 51 and 3 by 3.

Each group gets 17 markers and 1 board.

Well explained 👍

Problem 2

A school has 51 red chairs and 3 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

GCF of 51 and 3 is 3. So each row will have 3 chairs.

Explanation

There are 51 red and 3 blue chairs.

To find the total number of chairs in each row, we should find the GCF of 51 and 3.

There will be 3 chairs in each row.

Well explained 👍

Problem 3

A tailor has 51 meters of red ribbon and 3 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 51 and 3. The GCF of 51 and 3 is 3. Each piece of ribbon is 3 meters long.

Explanation

For calculating the longest length of the ribbon first we need to calculate the GCF of 51 and 3 which is 3.

The length of each piece of the ribbon will be 3 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 51 cm long and the other 3 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 51 and 3 is 3. The longest length of each piece is 3 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 51 cm and 3 cm, respectively, we have to find the GCF of 51 and 3, which is 3 cm.

The longest length of each piece is 3 cm.

Well explained 👍

Problem 5

If the GCF of 51 and ‘a’ is 3, and the LCM is 153, find ‘a’.

Okay, lets begin

The value of ‘a’ is 9.

Explanation

GCF x LCM = product of the numbers

3 × 153

= 51 × a 459

= 51a a

= 459 ÷ 51 = 9

Well explained 👍

FAQs on the Greatest Common Factor of 51 and 3

1.What is the LCM of 51 and 3?

The LCM of 51 and 3 is 51.

2.Is 51 divisible by 3?

Yes, 51 is divisible by 3 because the sum of its digits (5 + 1 = 6) is divisible by 3.

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 51?

The prime factorization of 51 is 3 x 17.

5.Are 51 and 3 prime numbers?

No, 51 is not a prime number because it has more than two factors, but 3 is a prime number because it has exactly two distinct positive divisors: 1 and itself.

Important Glossaries for GCF of 51 and 3

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 51 are 1, 3, 17, and 51.
  • 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 51 are 3 and 17.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 51 is divided by 3, the remainder is 0 and the quotient is 17.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 51 and 3 is 51.

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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.