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103 LearnersLast updated on September 9, 2025
GCF of 32 and 45
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 32 and 45.
What is the GCF of 32 and 45?
The greatest common factor of 32 and 45 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 32 and 45?
To find the GCF of 32 and 45, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 32 and 45 by Using Listing of Factors
Steps to find the GCF of 32 and 45 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 32 = 1, 2, 4, 8, 16, 32. Factors of 45 = 1, 3, 5, 9, 15, 45.
Step 2: Now, identify the common factors of them Common factor of 32 and 45: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 32 and 45 is 1.
GCF of 32 and 45 Using Prime Factorization
To find the GCF of 32 and 45 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 32: 32 = 2 x 2 x 2 x 2 x 2 = 2^5 Prime Factors of 45: 45 = 3 x 3 x 5 = 3^2 x 5
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Multiply the common prime factors Since there are no common prime factors, the GCF is 1. The Greatest Common Factor of 32 and 45 is 1.
GCF of 32 and 45 Using Division Method or Euclidean Algorithm Method
Find the GCF of 32 and 45 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 45 by 32 45 ÷ 32 = 1 (quotient), The remainder is calculated as 45 − (32×1) = 13 The remainder is 13, not zero, so continue the process
Step 2: Now divide the previous divisor (32) by the previous remainder (13) Divide 32 by 13 32 ÷ 13 = 2 (quotient), remainder = 32 − (13×2) = 6 Since the remainder is not zero, continue the process
Step 3: Now divide the previous divisor (13) by the previous remainder (6) Divide 13 by 6 13 ÷ 6 = 2 (quotient), remainder = 13 − (6×2) = 1 Since the remainder is not zero, continue the process
Step 4: Now divide the previous divisor (6) by the previous remainder (1) 6 ÷ 1 = 6 (quotient), remainder = 6 − (1×6) = 0 The remainder is zero, so the divisor will become the GCF.
The GCF of 32 and 45 is 1.
Common Mistakes and How to Avoid Them in GCF of 32 and 45
Finding the GCF of 32 and 45 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors. For example, while listing factors of 32, students may mention 10, which is incorrect.
To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the wrong common factor
Students may sometimes select the smallest common factor instead of the largest one.
To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers.
However, it does not affect the GCF, but it indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of Factors
Students confuse factors with multiples. In that confusion, sometimes they may write multiples instead of factors.
To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is always an even number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number.
To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 32 and 45 Examples
Problem 1
A gardener has 32 red roses and 45 white roses. She wants to create bouquets with the same number of roses of each color in each bouquet, using the largest possible number of bouquets. How many roses will each bouquet have?
We should find the GCF of 32 and 45 GCF of 32 and 45 is 1. There are 1 rose per bouquet. 32 ÷ 1 = 32 45 ÷ 1 = 45 There will be 1 bouquet, and each bouquet gets 32 red roses and 45 white roses.
Explanation
As the GCF of 32 and 45 is 1, the gardener can make only 1 bouquet with all the roses.
Problem 2
A library has 32 fiction books and 45 non-fiction books. They want to arrange them on shelves with the same number of books on each shelf, using the largest possible number of books per shelf. How many books will be on each shelf?
GCF of 32 and 45 is 1. So each shelf will have 1 book of each type.
Explanation
There are 32 fiction and 45 non-fiction books.
To find the total number of books on each shelf, we should find the GCF of 32 and 45.
There will be 1 book of each type on each shelf.
Problem 3
A tailor has 32 meters of silk fabric and 45 meters of cotton 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?
For calculating the longest equal length, we have to calculate the GCF of 32 and 45. The GCF of 32 and 45 is 1. The fabric is 1 meter long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 32 and 45, which is 1.
The length of each piece of the fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 32 cm long and the other 45 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?
The carpenter needs the longest piece of wood. GCF of 32 and 45 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, 32 cm and 45 cm, respectively, we have to find the GCF of 32 and 45, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 32 and ‘b’ is 1, and the LCM is 1440, find ‘b’.
The value of ‘b’ is 45.
Explanation
GCF x LCM = product of the numbers
1 × 1440
= 32 × b 1440
= 32b b
= 1440 ÷ 32 = 45
FAQs on the Greatest Common Factor of 32 and 45
1.What is the LCM of 32 and 45?
2.Is 32 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 45?
5.Are 32 and 45 prime numbers?
Important Glossaries for GCF of 32 and 45
- 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 5 are 5, 10, 15, 20, 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 20 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 5, the remainder is 4 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 5 and 10 is 10.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 18 and 24 will be 6, 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.
