HCF of 140 and 196
HCF of 140 and 196 is the largest possible number that divides 140 and 196 exactly without any remainder. The factors of 140 and 196 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140 and 1, 2, 4, 7, 14, 28, 49, 98, 196 respectively. There are 3 commonly used methods to find the HCF of 140 and 196  prime factorization, long division, and Euclidean algorithm.
1.  HCF of 140 and 196 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 140 and 196?
Answer: HCF of 140 and 196 is 28.
Explanation:
The HCF of two nonzero integers, x(140) and y(196), is the highest positive integer m(28) that divides both x(140) and y(196) without any remainder.
Methods to Find HCF of 140 and 196
Let's look at the different methods for finding the HCF of 140 and 196.
 Long Division Method
 Using Euclid's Algorithm
 Listing Common Factors
HCF of 140 and 196 by Long Division
HCF of 140 and 196 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 196 (larger number) by 140 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (140) by the remainder (56).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (28) is the HCF of 140 and 196.
HCF of 140 and 196 by Euclidean Algorithm
As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 196 and Y = 140
 HCF(196, 140) = HCF(140, 196 mod 140) = HCF(140, 56)
 HCF(140, 56) = HCF(56, 140 mod 56) = HCF(56, 28)
 HCF(56, 28) = HCF(28, 56 mod 28) = HCF(28, 0)
 HCF(28, 0) = 28 (∵ HCF(X, 0) = X, where X ≠ 0)
Therefore, the value of HCF of 140 and 196 is 28.
HCF of 140 and 196 by Listing Common Factors
 Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
 Factors of 196: 1, 2, 4, 7, 14, 28, 49, 98, 196
There are 6 common factors of 140 and 196, that are 1, 2, 4, 7, 14, and 28. Therefore, the highest common factor of 140 and 196 is 28.
☛ Also Check:
 HCF of 18 and 42 = 6
 HCF of 16 and 36 = 4
 HCF of 12 and 14 = 2
 HCF of 960 and 432 = 48
 HCF of 32 and 40 = 8
 HCF of 12, 18 and 24 = 6
 HCF of 1260 and 7344 = 36
HCF of 140 and 196 Examples

Example 1: Find the highest number that divides 140 and 196 exactly.
Solution:
The highest number that divides 140 and 196 exactly is their highest common factor, i.e. HCF of 140 and 196.
⇒ Factors of 140 and 196: Factors of 140 = 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
 Factors of 196 = 1, 2, 4, 7, 14, 28, 49, 98, 196
Therefore, the HCF of 140 and 196 is 28.

Example 2: The product of two numbers is 27440. If their HCF is 28, what is their LCM?
Solution:
Given: HCF = 28 and product of numbers = 27440
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 27440/28
Therefore, the LCM is 980. 
Example 3: Find the HCF of 140 and 196, if their LCM is 980.
Solution:
∵ LCM × HCF = 140 × 196
⇒ HCF(140, 196) = (140 × 196)/980 = 28
Therefore, the highest common factor of 140 and 196 is 28.
FAQs on HCF of 140 and 196
What is the HCF of 140 and 196?
The HCF of 140 and 196 is 28. To calculate the Highest common factor (HCF) of 140 and 196, we need to factor each number (factors of 140 = 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140; factors of 196 = 1, 2, 4, 7, 14, 28, 49, 98, 196) and choose the highest factor that exactly divides both 140 and 196, i.e., 28.
What are the Methods to Find HCF of 140 and 196?
There are three commonly used methods to find the HCF of 140 and 196.
 By Long Division
 By Listing Common Factors
 By Prime Factorization
What is the Relation Between LCM and HCF of 140, 196?
The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 140 and 196, i.e. HCF × LCM = 140 × 196.
How to Find the HCF of 140 and 196 by Prime Factorization?
To find the HCF of 140 and 196, we will find the prime factorization of the given numbers, i.e. 140 = 2 × 2 × 5 × 7; 196 = 2 × 2 × 7 × 7.
⇒ Since 2, 2, 7 are common terms in the prime factorization of 140 and 196. Hence, HCF(140, 196) = 2 × 2 × 7 = 28
☛ Prime Number
How to Find the HCF of 140 and 196 by Long Division Method?
To find the HCF of 140, 196 using long division method, 196 is divided by 140. The corresponding divisor (28) when remainder equals 0 is taken as HCF.
If the HCF of 196 and 140 is 28, Find its LCM.
HCF(196, 140) × LCM(196, 140) = 196 × 140
Since the HCF of 196 and 140 = 28
⇒ 28 × LCM(196, 140) = 27440
Therefore, LCM = 980
☛ Highest Common Factor Calculator
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