GCF of 45 and 60
2026-02-21 20:25 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 45 and 60.

What is the GCF of 45 and 60?

The greatest common factor of 45 and 60 is 15. 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 45 and 60?

To find the GCF of 45 and 60, a few methods are described below:

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

GCF of 45 and 60 by Using Listing of Factors

Steps to find the GCF of 45 and 60 using the listing of factors:

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

Factors of 45 = 1, 3, 5, 9, 15, 45.

Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

Step 2: Now, identify the common factors of them Common factors of 45 and 60: 1, 3, 5, 15.

Step 3: Choose the largest factor The largest factor that both numbers have is 15.

The GCF of 45 and 60 is 15.

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GCF of 45 and 60 Using Prime Factorization

To find the GCF of 45 and 60 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number:

Prime Factors of 45: 45 = 3 x 3 x 5 = 3² x 5

Prime Factors of 60: 60 = 2 x 2 x 3 x 5 = 2² x 3 x 5

Step 2: Now, identify the common prime factors

The common prime factors are: 3 x 5 = 3¹ x 5

Step 3: Multiply the common prime factors 3¹ x 5 = 3 x 5 = 15.

The Greatest Common Factor of 45 and 60 is 15.

GCF of 45 and 60 Using Division Method or Euclidean Algorithm Method

Find the GCF of 45 and 60 using the division method or Euclidean Algorithm Method. Follow these steps:

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


Here, divide 60 by 45 60 ÷ 45 = 1 (quotient),


The remainder is calculated as 60 − (45×1) = 15


The remainder is 15, not zero, so continue the process

Step 2: Now divide the previous divisor (45) by the previous remainder (15)

Divide 45 by 15 45 ÷ 15 = 3 (quotient), remainder = 45 − (15×3) = 0

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

The GCF of 45 and 60 is 15.

Common Mistakes and How to Avoid Them in GCF of 45 and 60

Finding GCF of 45 and 60 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 chef has 45 apples and 60 oranges. She wants to make fruit baskets with an equal number of fruits in each basket. How many fruits will be in each basket?

Okay, lets begin

We should find GCF of 45 and 60 GCF of 45 and 60

3 x 5 = 15.

There are 15 equal groups

45 ÷ 15 = 3

60 ÷ 15 = 4

There will be 15 baskets, and each basket gets 3 apples and 4 oranges.

Explanation

As the GCF of 45 and 60 is 15, the chef can make 15 baskets.

Now divide 45 and 60 by 15.

Each basket gets 3 apples and 4 oranges.

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Problem 2

A school has 45 red balloons and 60 blue balloons. They want to arrange them in columns with the same number of balloons in each column, using the largest possible number of balloons per column. How many balloons will be in each column?

Okay, lets begin

GCF of 45 and 60 3 x 5 = 15. So each column will have 15 balloons.

Explanation

There are 45 red and 60 blue balloons.

To find the total number of balloons in each column, we should find the GCF of 45 and 60.

There will be 15 balloons in each column.

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Problem 3

A tailor has 45 meters of red fabric and 60 meters of blue fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?

Okay, lets begin

For calculating longest equal length, we have to calculate the GCF of 45 and 60

The GCF of 45 and 60 3 x 5 = 15.

The fabric is 15 meters long.

Explanation

For calculating the longest length of the fabric, first we need to calculate the GCF of 45 and 60 which is 15. The length of each piece of the fabric will be 15 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 45 cm long and the other 60 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 45 and 60

3 x 5 = 15.

The longest length of each piece is 15 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 45 cm and 60 cm, respectively. We have to find the GCF of 45 and 60, which is 15 cm. The longest length of each piece is 15 cm.

Well explained 👍

Problem 5

If the GCF of 45 and ‘a’ is 15, and the LCM is 180. Find ‘a’.

Okay, lets begin

The value of ‘a’ is 60.

Explanation

GCF x LCM = product of the numbers

15 × 180 = 45 × a

2700 = 45a

a = 2700 ÷ 45 = 60

Well explained 👍

FAQs on the Greatest Common Factor of 45 and 60

1.What is the LCM of 45 and 60?

The LCM of 45 and 60 is 180.

2.Is 45 divisible by 3?

Yes, 45 is divisible by 3 because the sum of its digits (4 + 5) is 9, which 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 60?

The prime factorization of 60 is 2² x 3 x 5.

5.Are 45 and 60 prime numbers?

No, 45 and 60 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 45 and 60

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, 25, 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 45 are 3 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 45 and 60 is 180.
  • GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 45 and 60 will be 15, as it is their largest common factor that divides the numbers completely.

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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.