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107 LearnersLast updated on September 23, 2025
GCF of 49 and 64
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 49 and 64.
What is the GCF of 49 and 64?
The greatest common factor of 49 and 64 is 1. 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 49 and 64?
To find the GCF of 49 and 64, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 49 and 64 by Using Listing of Factors
Steps to find the GCF of 49 and 64 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 49 = 1, 7, 49.
Factors of 64 = 1, 2, 4, 8, 16, 32, 64.
Step 2: Now, identify the common factors of them Common factors of 49 and 64: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 49 and 64 is 1.
GCF of 49 and 64 Using Prime Factorization
To find the GCF of 49 and 64 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime Factors of each number
Prime Factors of 49 : 49 = 7 x 7 = 7²
Prime Factors of 64 : 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2⁶
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.
GCF of 49 and 64 Using Division Method or Euclidean Algorithm Method
Find the GCF of 49 and 64 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 64 by 49 64 ÷ 49 = 1 (quotient), The remainder is calculated as 64 - (49×1) = 15
The remainder is 15, not zero, so continue the process
Step 2: Now divide the previous divisor (49) by the previous remainder (15) 49 ÷ 15 = 3 (quotient), remainder = 49 - (15×3) = 4
Step 3: Continue the process by dividing the previous divisor (15)
by the previous remainder (4) 15 ÷ 4 = 3 (quotient), remainder = 15 - (4×3) = 3
Continue dividing 4 by 3 4 ÷ 3 = 1 (quotient), remainder = 4 - (3×1) = 1
Continue dividing 3 by 1 3 ÷ 1 = 3 (quotient), remainder = 3 - (1×3) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 49 and 64 is 1.
Common Mistakes and How to Avoid Them in GCF of 49 and 64
Finding the GCF of 49 and 64 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 49, students may mention 14, 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. Since 49 and 64 are co-prime, the GCF is 1, which is both the smallest and largest common factor.
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 and 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 greater than 1
Students may assume that the GCF of two numbers is always greater than 1. But it's not true; the GCF can be 1, especially in co-prime numbers. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 49 and 64 Examples
Problem 1
A gardener has a 49-meter roll of wire and a 64-meter roll of netting. He wants to cut them into pieces of equal length, with the longest possible length. How long should each piece be?
We should find the GCF of 49 and 64 The GCF of 49 and 64 is 1.
Each piece will be 1 meter long.
Explanation
As the GCF of 49 and 64 is 1, the gardener can cut each roll into pieces of 1 meter in length.
Problem 2
A baker has 49 cupcakes and 64 cookies. He wants to package them in boxes with the same number of items in each box, using the largest possible number of items per box. How many items will be in each box?
GCF of 49 and 64 is 1.
So each box will have 1 item.
Explanation
There are 49 cupcakes and 64 cookies.
To find the total number of items in each box, we should find the GCF of 49 and 64.
There will be 1 item in each box.
Problem 3
A seamstress has 49 meters of fabric in one color and 64 meters in another. 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 49 and 64 The GCF of 49 and 64 is 1.
The fabric is cut into pieces 1 meter long.
Explanation
For calculating the longest length of the fabric first, we need to calculate the GCF of 49 and 64, which is 1. The length of each piece of the fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 49 cm long and the other 64 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 49 and 64 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, 49 cm and 64 cm, respectively, we have to find the GCF of 49 and 64, which is 1 cm. The longest length of each piece is 1 cm.
Problem 5
If the GCF of 49 and ‘b’ is 1, and the LCM is 49b, find the value of ‘b’.
The value of ‘b’ is 64.
Explanation
GCF x LCM = product of the numbers 1 × 49b = 49 × b 49b = 49b
This equation is always true, so b can be any number that is co-prime with 49 and results in the LCM equation being satisfied.
FAQs on the Greatest Common Factor of 49 and 64
1.What is the LCM of 49 and 64?
2.Is 49 divisible by 7?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 64?
5.Are 49 and 64 co-prime numbers?
Important Glossaries for GCF of 49 and 64
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 49 are 1, 7, and 49.
- Co-prime Numbers: Two numbers are co-prime if their greatest common factor (GCF) is 1. For example, 49 and 64 are co-prime.
- 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 49 are 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 49 is divided by 64, the remainder is 49.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 49 and 64 is 3136.
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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.
