GCF of 140 and 180
GCF of 140 and 180 is the largest possible number that divides 140 and 180 exactly without any remainder. The factors of 140 and 180 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140 and 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 respectively. There are 3 commonly used methods to find the GCF of 140 and 180  prime factorization, long division, and Euclidean algorithm.
1.  GCF of 140 and 180 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 140 and 180?
Answer: GCF of 140 and 180 is 20.
Explanation:
The GCF of two nonzero integers, x(140) and y(180), is the greatest positive integer m(20) that divides both x(140) and y(180) without any remainder.
Methods to Find GCF of 140 and 180
Let's look at the different methods for finding the GCF of 140 and 180.
 Using Euclid's Algorithm
 Long Division Method
 Prime Factorization Method
GCF of 140 and 180 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 = 180 and Y = 140
 GCF(180, 140) = GCF(140, 180 mod 140) = GCF(140, 40)
 GCF(140, 40) = GCF(40, 140 mod 40) = GCF(40, 20)
 GCF(40, 20) = GCF(20, 40 mod 20) = GCF(20, 0)
 GCF(20, 0) = 20 (∵ GCF(X, 0) = X, where X ≠ 0)
Therefore, the value of GCF of 140 and 180 is 20.
GCF of 140 and 180 by Long Division
GCF of 140 and 180 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 180 (larger number) by 140 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (140) by the remainder (40).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (20) is the GCF of 140 and 180.
GCF of 140 and 180 by Prime Factorization
Prime factorization of 140 and 180 is (2 × 2 × 5 × 7) and (2 × 2 × 3 × 3 × 5) respectively. As visible, 140 and 180 have common prime factors. Hence, the GCF of 140 and 180 is 2 × 2 × 5 = 20.
☛ Also Check:
 GCF of 12 and 9 = 3
 GCF of 3 and 12 = 3
 GCF of 50 and 72 = 2
 GCF of 63 and 72 = 9
 GCF of 7 and 9 = 1
 GCF of 15 and 27 = 3
 GCF of 4 and 10 = 2
GCF of 140 and 180 Examples

Example 1: Find the GCF of 140 and 180, if their LCM is 1260.
Solution:
∵ LCM × GCF = 140 × 180
⇒ GCF(140, 180) = (140 × 180)/1260 = 20
Therefore, the greatest common factor of 140 and 180 is 20. 
Example 2: For two numbers, GCF = 20 and LCM = 1260. If one number is 140, find the other number.
Solution:
Given: GCF (x, 140) = 20 and LCM (x, 140) = 1260
∵ GCF × LCM = 140 × (x)
⇒ x = (GCF × LCM)/140
⇒ x = (20 × 1260)/140
⇒ x = 180
Therefore, the other number is 180. 
Example 3: Find the greatest number that divides 140 and 180 exactly.
Solution:
The greatest number that divides 140 and 180 exactly is their greatest common factor, i.e. GCF of 140 and 180.
⇒ Factors of 140 and 180: Factors of 140 = 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
 Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Therefore, the GCF of 140 and 180 is 20.
FAQs on GCF of 140 and 180
What is the GCF of 140 and 180?
The GCF of 140 and 180 is 20. To calculate the greatest common factor (GCF) of 140 and 180, we need to factor each number (factors of 140 = 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140; factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180) and choose the greatest factor that exactly divides both 140 and 180, i.e., 20.
What are the Methods to Find GCF of 140 and 180?
There are three commonly used methods to find the GCF of 140 and 180.
 By Prime Factorization
 By Long Division
 By Listing Common Factors
If the GCF of 180 and 140 is 20, Find its LCM.
GCF(180, 140) × LCM(180, 140) = 180 × 140
Since the GCF of 180 and 140 = 20
⇒ 20 × LCM(180, 140) = 25200
Therefore, LCM = 1260
☛ Greatest Common Factor Calculator
How to Find the GCF of 140 and 180 by Long Division Method?
To find the GCF of 140, 180 using long division method, 180 is divided by 140. The corresponding divisor (20) when remainder equals 0 is taken as GCF.
How to Find the GCF of 140 and 180 by Prime Factorization?
To find the GCF of 140 and 180, we will find the prime factorization of the given numbers, i.e. 140 = 2 × 2 × 5 × 7; 180 = 2 × 2 × 3 × 3 × 5.
⇒ Since 2, 2, 5 are common terms in the prime factorization of 140 and 180. Hence, GCF(140, 180) = 2 × 2 × 5 = 20
☛ Prime Number
What is the Relation Between LCM and GCF of 140, 180?
The following equation can be used to express the relation between Least Common Multiple and GCF of 140 and 180, i.e. GCF × LCM = 140 × 180.
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