HCF of 20, 30 and 40
HCF of 20, 30 and 40 is the largest possible number that divides 20, 30 and 40 exactly without any remainder. The factors of 20, 30 and 40 are (1, 2, 4, 5, 10, 20), (1, 2, 3, 5, 6, 10, 15, 30) and (1, 2, 4, 5, 8, 10, 20, 40) respectively. There are 3 commonly used methods to find the HCF of 20, 30 and 40  prime factorization, long division, and Euclidean algorithm.
1.  HCF of 20, 30 and 40 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 20, 30 and 40?
Answer: HCF of 20, 30 and 40 is 10.
Explanation:
The HCF of three nonzero integers, x(20), y(30) and z(40), is the highest positive integer m(10) that divides x(20), y(30) and z(40) without any remainder.
Methods to Find HCF of 20, 30 and 40
Let's look at the different methods for finding the HCF of 20, 30 and 40.
 Listing Common Factors
 Long Division Method
 Prime Factorization Method
HCF of 20, 30 and 40 by Listing Common Factors
 Factors of 20: 1, 2, 4, 5, 10, 20
 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
 Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
There are 4 common factors of 20, 30 and 40, that are 1, 2, 10, and 5. Therefore, the highest common factor of 20, 30 and 40 is 10.
HCF of 20, 30 and 40 by Long Division
HCF of 20, 30 and 40 can be represented as HCF of (HCF of 20, 30) and 40. HCF(20, 30, 40) can be thus calculated by first finding HCF(20, 30) using long division and thereafter using this result with 40 to perform long division again.
 Step 1: Divide 30 (larger number) by 20 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (10). Repeat this process until the remainder = 0.
⇒ HCF(20, 30) = 10.  Step 3: Now to find the HCF of 10 and 40, we will perform a long division on 40 and 10.
 Step 4: For remainder = 0, divisor = 10 ⇒ HCF(10, 40) = 10
Thus, HCF(20, 30, 40) = HCF(HCF(20, 30), 40) = 10.
HCF of 20, 30 and 40 by Prime Factorization
Prime factorization of 20, 30 and 40 is (2 × 2 × 5), (2 × 3 × 5) and (2 × 2 × 2 × 5) respectively. As visible, 20, 30 and 40 have common prime factors. Hence, the HCF of 20, 30 and 40 is 2 × 5 = 10.
☛ Also Check:
 HCF of 1001 and 910 = 91
 HCF of 72, 108 and 180 = 36
 HCF of 56 and 84 = 28
 HCF of 20, 28 and 36 = 4
 HCF of 15 and 20 = 5
 HCF of 657 and 963 = 9
 HCF of 24, 36 and 40 = 4
HCF of 20, 30 and 40 Examples

Example 1: Calculate the HCF of 20, 30, and 40 using LCM of the given numbers.
Solution:
Prime factorization of 20, 30 and 40 is given as,
 20 = 2 × 2 × 5
 30 = 2 × 3 × 5
 40 = 2 × 2 × 2 × 5
LCM(20, 30) = 60, LCM(30, 40) = 120, LCM(40, 20) = 40, LCM(20, 30, 40) = 120
⇒ HCF(20, 30, 40) = [(20 × 30 × 40) × LCM(20, 30, 40)]/[LCM(20, 30) × LCM (30, 40) × LCM(40, 20)]
⇒ HCF(20, 30, 40) = (24000 × 120)/(60 × 120 × 40)
⇒ HCF(20, 30, 40) = 10.
Therefore, the HCF of 20, 30 and 40 is 10. 
Example 2: Verify the relation between the LCM and HCF of 20, 30 and 40.
Solution:
The relation between the LCM and HCF of 20, 30 and 40 is given as, HCF(20, 30, 40) = [(20 × 30 × 40) × LCM(20, 30, 40)]/[LCM(20, 30) × LCM (30, 40) × LCM(20, 40)]
⇒ Prime factorization of 20, 30 and 40: 20 = 2 × 2 × 5
 30 = 2 × 3 × 5
 40 = 2 × 2 × 2 × 5
∴ LCM of (20, 30), (30, 40), (20, 40), and (20, 30, 40) is 60, 120, 40, and 120 respectively.
Now, LHS = HCF(20, 30, 40) = 10.
And, RHS = [(20 × 30 × 40) × LCM(20, 30, 40)]/[LCM(20, 30) × LCM (30, 40) × LCM(20, 40)] = [(24000) × 120]/[60 × 120 × 40]
LHS = RHS = 10.
Hence verified. 
Example 3: Find the highest number that divides 20, 30, and 40 completely.
Solution:
The highest number that divides 20, 30, and 40 exactly is their highest common factor.
 Factors of 20 = 1, 2, 4, 5, 10, 20
 Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
 Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
The HCF of 20, 30, and 40 is 10.
∴ The highest number that divides 20, 30, and 40 is 10.
FAQs on HCF of 20, 30 and 40
What is the HCF of 20, 30 and 40?
The HCF of 20, 30 and 40 is 10. To calculate the highest common factor (HCF) of 20, 30 and 40, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the highest factor that exactly divides 20, 30 and 40, i.e., 10.
Which of the following is HCF of 20, 30 and 40? 10, 79, 51, 88, 54, 83, 62, 41
HCF of 20, 30, 40 will be the number that divides 20, 30, and 40 without leaving any remainder. The only number that satisfies the given condition is 10.
How to Find the HCF of 20, 30 and 40 by Prime Factorization?
To find the HCF of 20, 30 and 40, we will find the prime factorization of given numbers, i.e. 20 = 2 × 2 × 5; 30 = 2 × 3 × 5; 40 = 2 × 2 × 2 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 20, 30 and 40. Hence, HCF(20, 30, 40) = 2 × 5 = 10
☛ What is a Prime Number?
What are the Methods to Find HCF of 20, 30 and 40?
There are three commonly used methods to find the HCF of 20, 30 and 40.
 By Long Division
 By Prime Factorization
 By Listing Common Factors
What is the Relation Between LCM and HCF of 20, 30 and 40?
The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 20, 30 and 40, i.e. HCF(20, 30, 40) = [(20 × 30 × 40) × LCM(20, 30, 40)]/[LCM(20, 30) × LCM (30, 40) × LCM(20, 40)].
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