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102 LearnersLast updated on September 24, 2025
GCF of 61 and 73
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 61 and 73.
What is the GCF of 61 and 73?
The greatest common factor of 61 and 73 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 61 and 73?
To find the GCF of 61 and 73, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 61 and 73 by Using Listing of factors
Steps to find the GCF of 61 and 73 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 61 = 1, 61. Factors of 73 = 1, 73.
Step 2: Now, identify the common factors of them Common factors of 61 and 73: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 61 and 73 is 1.
GCF of 61 and 73 Using Prime Factorization
To find the GCF of 61 and 73 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 61: 61 is a prime number. Prime Factors of 73: 73 is a prime number.
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Since there are no common prime factors, the Greatest Common Factor of 61 and 73 is 1.
GCF of 61 and 73 Using Division Method or Euclidean Algorithm Method
Find the GCF of 61 and 73 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 73 by 61 73 ÷ 61 = 1 (quotient), The remainder is calculated as 73 − (61×1) = 12 The remainder is 12, not zero, so continue the process
Step 2: Now divide the previous divisor (61) by the previous remainder (12) 61 ÷ 12 = 5 (quotient), remainder = 61 − (12×5) = 1 The remainder is 1, not zero, so continue the process
Step 3: Now divide 12 by 1 12 ÷ 1 = 12 (quotient), remainder = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 61 and 73 is 1.
Common Mistakes and How to Avoid Them in GCF of 61 and 73
Finding the GCF of 61 and 73 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 61, students may mention 2 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. This 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 that 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 61 and 73 Examples
Problem 1
A gardener has 61 tulip bulbs and 73 rose bulbs. She wants to arrange them in the largest number of equal groups possible. How many bulbs will be in each group?
We should find the GCF of 61 and 73 GCF of 61 and 73 is 1. There are 1 equal groups 61 ÷ 1 = 61 73 ÷ 1 = 73 There will be 1 group, and each group gets 61 tulip bulbs and 73 rose bulbs.
Explanation
As the GCF of 61 and 73 is 1, the gardener can make 1 group.
Now divide 61 and 73 by 1.
Each group gets 61 tulip bulbs and 73 rose bulbs.
Problem 2
A chef has 61 apples and 73 oranges. He wants to place them in rows with the same number of fruits in each row, using the largest possible number of fruits per row. How many fruits will be in each row?
GCF of 61 and 73 is 1. So each row will have 1 fruit.
Explanation
There are 61 apples and 73 oranges.
To find the total number of fruits in each row, we should find the GCF of 61 and 73.
There will be 1 fruit in each row.
Problem 3
A tailor has 61 meters of cotton fabric and 73 meters of silk 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 61 and 73. The GCF of 61 and 73 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 61 and 73 which is 1.
The length of each piece of fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 61 cm long and the other 73 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 61 and 73 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, 61 cm and 73 cm, respectively.
We have to find the GCF of 61 and 73, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 61 and ‘b’ is 1, and the LCM is 4453. Find ‘b’.
The value of ‘b’ is 73.
Explanation
GCF x LCM = Product of the numbers
1 × 4453 = 61 × b
4453 = 61b
b = 4453 ÷ 61
= 73
FAQs on the Greatest Common Factor of 61 and 73
1.What is the LCM of 61 and 73?
2.Is 61 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 73?
5.Are 61 and 73 prime numbers?
Important Glossaries for GCF of 61 and 73
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Prime Number: A number greater than 1 that has no positive divisors other than 1 and itself. For example, 61 and 73 are prime numbers.
- Co-prime Numbers: Two numbers having no common factors other than 1. For example, 61 and 73 are co-prime numbers.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 61 and 73 is 4453.
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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.
