HCF of 5, 10 and 15

HCF of 5, 10 and 15 is the largest possible number that divides 5, 10 and 15 exactly without any remainder. The factors of 5, 10 and 15 are (1, 5), (1, 2, 5, 10) and (1, 3, 5, 15) respectively. There are 3 commonly used methods to find the HCF of 5, 10 and 15 - prime factorization, Euclidean algorithm, and long division.

Answer: HCF of 5, 10 and 15 is 5.

Explanation:

The HCF of three non-zero integers, x(5), y(10) and z(15), is the highest positive integer m(5) that divides x(5), y(10) and z(15) without any remainder.

Let's look at the different methods for finding the HCF of 5, 10 and 15.

• Long Division Method
• Prime Factorization Method
• Using Euclid's Algorithm

HCF of 5, 10 and 15 by Long Division

HCF of 5, 10 and 15 can be represented as HCF of (HCF of 5, 10) and 15. HCF(5, 10, 15) can be thus calculated by first finding HCF(5, 10) using long division and thereafter using this result with 15 to perform long division again.

• Step 1: Divide 10 (larger number) by 5 (smaller number).
• Step 2: Since the remainder = 0, the divisor (5) is the HCF(5, 10) = 5.
• Step 3: Now to find the HCF of 5 and 15, we will perform a long division on 15 and 5.
• Step 4: For remainder = 0, divisor = 5 ⇒ HCF(5, 15) = 5

Thus, HCF(5, 10, 15) = HCF(HCF(5, 10), 15) = 5.

HCF of 5, 10 and 15 by Prime Factorization

Prime factorization of 5, 10 and 15 is (5), (2 × 5) and (3 × 5) respectively. As visible, 5, 10 and 15 have only one common prime factor i.e. 5. Hence, the HCF of 5, 10 and 15 is 5.

HCF of 5, 10 and 15 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(5, 10, 15) = HCF(HCF(5, 10), 15)

• 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, 15)

• HCF(15, 5) = HCF(5, 15 mod 5) = HCF(5, 0)
• HCF(5, 0) = 5 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 5, 10 and 15 is 5.

☛ Also Check:

• HCF of 27 and 36 = 9
• HCF of 5 and 10 = 5
• HCF of 2 and 5 = 1
• HCF of 140 and 196 = 28
• HCF of 777, 315 and 588 = 21
• HCF of 36, 42 and 48 = 6
• HCF of 14 and 15 = 1

FAQs on HCF of 5, 10 and 15

What is the HCF of 5, 10 and 15?

The HCF of 5, 10 and 15 is 5. To calculate the HCF of 5, 10 and 15, we need to factor each number (factors of 5 = 1, 5; factors of 10 = 1, 2, 5, 10; factors of 15 = 1, 3, 5, 15) and choose the highest factor that exactly divides 5, 10 and 15, i.e., 5.

What is the Relation Between LCM and HCF of 5, 10 and 15?

The following equation can be used to express the relation between Least Common Multiple and HCF of 5, 10 and 15, i.e. HCF(5, 10, 15) = [(5 × 10 × 15) × LCM(5, 10, 15)]/[LCM(5, 10) × LCM (10, 15) × LCM(5, 15)].
☛ Highest Common Factor Calculator

Which of the following is HCF of 5, 10 and 15? 5, 55, 49, 57, 32

HCF of 5, 10, 15 will be the number that divides 5, 10, and 15 without leaving any remainder. The only number that satisfies the given condition is 5.

What are the Methods to Find HCF of 5, 10 and 15?

There are three commonly used methods to find the HCF of 5, 10 and 15.

• By Long Division
• By Euclidean Algorithm
• By Prime Factorization

How to Find the HCF of 5, 10 and 15 by Prime Factorization?

To find the HCF of 5, 10 and 15, we will find the prime factorization of given numbers, i.e. 5 = 5; 10 = 2 × 5; 15 = 3 × 5.
⇒ Since 5 is the only common prime factor of 5, 10 and 15. Hence, HCF(5, 10, 15) = 5.
☛ What are Prime Numbers?