HCF of 15, 25 and 30
HCF of 15, 25 and 30 is the largest possible number that divides 15, 25 and 30 exactly without any remainder. The factors of 15, 25 and 30 are (1, 3, 5, 15), (1, 5, 25) and (1, 2, 3, 5, 6, 10, 15, 30) respectively. There are 3 commonly used methods to find the HCF of 15, 25 and 30  Euclidean algorithm, long division, and prime factorization.
1.  HCF of 15, 25 and 30 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 15, 25 and 30?
Answer: HCF of 15, 25 and 30 is 5.
Explanation:
The HCF of three nonzero integers, x(15), y(25) and z(30), is the highest positive integer m(5) that divides x(15), y(25) and z(30) without any remainder.
Methods to Find HCF of 15, 25 and 30
The methods to find the HCF of 15, 25 and 30 are explained below.
 Listing Common Factors
 Prime Factorization Method
 Using Euclid's Algorithm
HCF of 15, 25 and 30 by Listing Common Factors
 Factors of 15: 1, 3, 5, 15
 Factors of 25: 1, 5, 25
 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
There are 2 common factors of 15, 25 and 30, that are 1 and 5. Therefore, the highest common factor of 15, 25 and 30 is 5.
HCF of 15, 25 and 30 by Prime Factorization
Prime factorization of 15, 25 and 30 is (3 × 5), (5 × 5) and (2 × 3 × 5) respectively. As visible, 15, 25 and 30 have only one common prime factor i.e. 5. Hence, the HCF of 15, 25 and 30 is 5.
HCF of 15, 25 and 30 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.
HCF(15, 25, 30) = HCF(HCF(15, 25), 30)
 HCF(25, 15) = HCF(15, 25 mod 15) = HCF(15, 10)
 HCF(15, 10) = HCF(10, 15 mod 10) = HCF(10, 5)
 HCF(10, 5) = HCF(5, 10 mod 5) = HCF(5, 0)
 HCF(5, 0) = 5 (∵ HCF(X, 0) = X, where X ≠ 0)
Steps for HCF(5, 30)
 HCF(30, 5) = HCF(5, 30 mod 5) = HCF(5, 0)
 HCF(5, 0) = 5 (∵ HCF(X, 0) = X, where X ≠ 0)
Therefore, the value of HCF of 15, 25 and 30 is 5.
☛ Also Check:
 HCF of 87 and 145 = 29
 HCF of 12 and 16 = 4
 HCF of 96 and 120 = 24
 HCF of 14 and 21 = 7
 HCF of 3556 and 3444 = 28
 HCF of 12 and 20 = 4
 HCF of 870 and 225 = 15
HCF of 15, 25 and 30 Examples

Example 1: Calculate the HCF of 15, 25, and 30 using LCM of the given numbers.
Solution:
Prime factorization of 15, 25 and 30 is given as,
 15 = 3 × 5
 25 = 5 × 5
 30 = 2 × 3 × 5
LCM(15, 25) = 75, LCM(25, 30) = 150, LCM(30, 15) = 30, LCM(15, 25, 30) = 150
⇒ HCF(15, 25, 30) = [(15 × 25 × 30) × LCM(15, 25, 30)]/[LCM(15, 25) × LCM (25, 30) × LCM(30, 15)]
⇒ HCF(15, 25, 30) = (11250 × 150)/(75 × 150 × 30)
⇒ HCF(15, 25, 30) = 5.
Therefore, the HCF of 15, 25 and 30 is 5. 
Example 2: Verify the relation between the LCM and HCF of 15, 25 and 30.
Solution:
The relation between the LCM and HCF of 15, 25 and 30 is given as, HCF(15, 25, 30) = [(15 × 25 × 30) × LCM(15, 25, 30)]/[LCM(15, 25) × LCM (25, 30) × LCM(15, 30)]
⇒ Prime factorization of 15, 25 and 30: 15 = 3 × 5
 25 = 5 × 5
 30 = 2 × 3 × 5
∴ LCM of (15, 25), (25, 30), (15, 30), and (15, 25, 30) is 75, 150, 30, and 150 respectively.
Now, LHS = HCF(15, 25, 30) = 5.
And, RHS = [(15 × 25 × 30) × LCM(15, 25, 30)]/[LCM(15, 25) × LCM (25, 30) × LCM(15, 30)] = [(11250) × 150]/[75 × 150 × 30]
LHS = RHS = 5.
Hence verified. 
Example 3: Find the highest number that divides 15, 25, and 30 completely.
Solution:
The highest number that divides 15, 25, and 30 exactly is their highest common factor.
 Factors of 15 = 1, 3, 5, 15
 Factors of 25 = 1, 5, 25
 Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
The HCF of 15, 25, and 30 is 5.
∴ The highest number that divides 15, 25, and 30 is 5.
FAQs on HCF of 15, 25 and 30
What is the HCF of 15, 25 and 30?
The HCF of 15, 25 and 30 is 5. To calculate the highest common factor (HCF) of 15, 25 and 30, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 25 = 1, 5, 25; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the highest factor that exactly divides 15, 25 and 30, i.e., 5.
Which of the following is HCF of 15, 25 and 30? 5, 39, 57, 77, 50, 68
HCF of 15, 25, 30 will be the number that divides 15, 25, and 30 without leaving any remainder. The only number that satisfies the given condition is 5.
What is the Relation Between LCM and HCF of 15, 25 and 30?
The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 15, 25 and 30, i.e. HCF(15, 25, 30) = [(15 × 25 × 30) × LCM(15, 25, 30)]/[LCM(15, 25) × LCM (25, 30) × LCM(15, 30)].
☛ HCF Calculator
How to Find the HCF of 15, 25 and 30 by Prime Factorization?
To find the HCF of 15, 25 and 30, we will find the prime factorization of given numbers, i.e. 15 = 3 × 5; 25 = 5 × 5; 30 = 2 × 3 × 5.
⇒ Since 5 is the only common prime factor of 15, 25 and 30. Hence, HCF(15, 25, 30) = 5.
☛ What are Prime Numbers?
What are the Methods to Find HCF of 15, 25 and 30?
There are three commonly used methods to find the HCF of 15, 25 and 30.
 By Long Division
 By Prime Factorization
 By Euclidean Algorithm
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