GCF of 64 and 144
GCF of 64 and 144 is the largest possible number that divides 64 and 144 exactly without any remainder. The factors of 64 and 144 are 1, 2, 4, 8, 16, 32, 64 and 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 respectively. There are 3 commonly used methods to find the GCF of 64 and 144  Euclidean algorithm, long division, and prime factorization.
1.  GCF of 64 and 144 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 64 and 144?
Answer: GCF of 64 and 144 is 16.
Explanation:
The GCF of two nonzero integers, x(64) and y(144), is the greatest positive integer m(16) that divides both x(64) and y(144) without any remainder.
Methods to Find GCF of 64 and 144
Let's look at the different methods for finding the GCF of 64 and 144.
 Listing Common Factors
 Using Euclid's Algorithm
 Long Division Method
GCF of 64 and 144 by Listing Common Factors
 Factors of 64: 1, 2, 4, 8, 16, 32, 64
 Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
There are 5 common factors of 64 and 144, that are 1, 2, 4, 8, and 16. Therefore, the greatest common factor of 64 and 144 is 16.
GCF of 64 and 144 by Euclidean Algorithm
As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 144 and Y = 64
 GCF(144, 64) = GCF(64, 144 mod 64) = GCF(64, 16)
 GCF(64, 16) = GCF(16, 64 mod 16) = GCF(16, 0)
 GCF(16, 0) = 16 (∵ GCF(X, 0) = X, where X ≠ 0)
Therefore, the value of GCF of 64 and 144 is 16.
GCF of 64 and 144 by Long Division
GCF of 64 and 144 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 144 (larger number) by 64 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (64) by the remainder (16).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (16) is the GCF of 64 and 144.
☛ Also Check:
 GCF of 35, 56 and 63 = 7
 GCF of 15 and 40 = 5
 GCF of 56 and 35 = 7
 GCF of 32 and 81 = 1
 GCF of 18 and 21 = 3
 GCF of 30 and 105 = 15
 GCF of 36 and 54 = 18
GCF of 64 and 144 Examples

Example 1: For two numbers, GCF = 16 and LCM = 576. If one number is 64, find the other number.
Solution:
Given: GCF (x, 64) = 16 and LCM (x, 64) = 576
∵ GCF × LCM = 64 × (x)
⇒ x = (GCF × LCM)/64
⇒ x = (16 × 576)/64
⇒ x = 144
Therefore, the other number is 144. 
Example 2: Find the GCF of 64 and 144, if their LCM is 576.
Solution:
∵ LCM × GCF = 64 × 144
⇒ GCF(64, 144) = (64 × 144)/576 = 16
Therefore, the greatest common factor of 64 and 144 is 16. 
Example 3: The product of two numbers is 9216. If their GCF is 16, what is their LCM?
Solution:
Given: GCF = 16 and product of numbers = 9216
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 9216/16
Therefore, the LCM is 576.
FAQs on GCF of 64 and 144
What is the GCF of 64 and 144?
The GCF of 64 and 144 is 16. To calculate the GCF (Greatest Common Factor) of 64 and 144, we need to factor each number (factors of 64 = 1, 2, 4, 8, 16, 32, 64; factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144) and choose the greatest factor that exactly divides both 64 and 144, i.e., 16.
How to Find the GCF of 64 and 144 by Prime Factorization?
To find the GCF of 64 and 144, we will find the prime factorization of the given numbers, i.e. 64 = 2 × 2 × 2 × 2 × 2 × 2; 144 = 2 × 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 2, 2 are common terms in the prime factorization of 64 and 144. Hence, GCF(64, 144) = 2 × 2 × 2 × 2 = 16
☛ Prime Numbers
How to Find the GCF of 64 and 144 by Long Division Method?
To find the GCF of 64, 144 using long division method, 144 is divided by 64. The corresponding divisor (16) when remainder equals 0 is taken as GCF.
What is the Relation Between LCM and GCF of 64, 144?
The following equation can be used to express the relation between Least Common Multiple and GCF of 64 and 144, i.e. GCF × LCM = 64 × 144.
What are the Methods to Find GCF of 64 and 144?
There are three commonly used methods to find the GCF of 64 and 144.
 By Long Division
 By Prime Factorization
 By Euclidean Algorithm
If the GCF of 144 and 64 is 16, Find its LCM.
GCF(144, 64) × LCM(144, 64) = 144 × 64
Since the GCF of 144 and 64 = 16
⇒ 16 × LCM(144, 64) = 9216
Therefore, LCM = 576
☛ Greatest Common Factor Calculator
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