HCF of 12, 15 and 18

HCF of 12, 15 and 18 is the largest possible number that divides 12, 15 and 18 exactly without any remainder. The factors of 12, 15 and 18 are (1, 2, 3, 4, 6, 12), (1, 3, 5, 15) and (1, 2, 3, 6, 9, 18) respectively. There are 3 commonly used methods to find the HCF of 12, 15 and 18 - Euclidean algorithm, prime factorization, and long division.

Answer: HCF of 12, 15 and 18 is 3.

Explanation:

The HCF of three non-zero integers, x(12), y(15) and z(18), is the highest positive integer m(3) that divides x(12), y(15) and z(18) without any remainder.

Let's look at the different methods for finding the HCF of 12, 15 and 18.

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

HCF of 12, 15 and 18 by Prime Factorization

Prime factorization of 12, 15 and 18 is (2 × 2 × 3), (3 × 5) and (2 × 3 × 3) respectively. As visible, 12, 15 and 18 have only one common prime factor i.e. 3. Hence, the HCF of 12, 15 and 18 is 3.

HCF of 12, 15 and 18 by Long Division

HCF of 12, 15 and 18 can be represented as HCF of (HCF of 12, 15) and 18. HCF(12, 15, 18) can be thus calculated by first finding HCF(12, 15) using long division and thereafter using this result with 18 to perform long division again.

• Step 1: Divide 15 (larger number) by 12 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (3). Repeat this process until the remainder = 0.
  ⇒ HCF(12, 15) = 3.
• Step 3: Now to find the HCF of 3 and 18, we will perform a long division on 18 and 3.
• Step 4: For remainder = 0, divisor = 3 ⇒ HCF(3, 18) = 3

Thus, HCF(12, 15, 18) = HCF(HCF(12, 15), 18) = 3.

HCF of 12, 15 and 18 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(12, 15, 18) = HCF(HCF(12, 15), 18)

• HCF(15, 12) = HCF(12, 15 mod 12) = HCF(12, 3)
• HCF(12, 3) = HCF(3, 12 mod 3) = HCF(3, 0)
• HCF(3, 0) = 3 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Steps for HCF(3, 18)

• HCF(18, 3) = HCF(3, 18 mod 3) = HCF(3, 0)
• HCF(3, 0) = 3 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 12, 15 and 18 is 3.

☛ Also Check:

• HCF of 0 and 6 = 6
• HCF of 391, 425 and 527 = 17
• HCF of 7 and 8 = 1
• HCF of 84 and 98 = 14
• HCF of 90 and 120 = 30
• HCF of 12, 36 and 48 = 12
• HCF of 20 and 35 = 5

FAQs on HCF of 12, 15 and 18

What is the HCF of 12, 15 and 18?

The HCF of 12, 15 and 18 is 3. To calculate the HCF (Highest Common Factor) of 12, 15 and 18, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 15 = 1, 3, 5, 15; factors of 18 = 1, 2, 3, 6, 9, 18) and choose the highest factor that exactly divides 12, 15 and 18, i.e., 3.

What is the Relation Between LCM and HCF of 12, 15 and 18?

The following equation can be used to express the relation between Least Common Multiple and HCF of 12, 15 and 18, i.e. HCF(12, 15, 18) = [(12 × 15 × 18) × LCM(12, 15, 18)]/[LCM(12, 15) × LCM (15, 18) × LCM(12, 18)].
☛ Highest Common Factor Calculator

Which of the following is HCF of 12, 15 and 18? 3, 29, 62, 22, 46

HCF of 12, 15, 18 will be the number that divides 12, 15, and 18 without leaving any remainder. The only number that satisfies the given condition is 3.

What are the Methods to Find HCF of 12, 15 and 18?

There are three commonly used methods to find the HCF of 12, 15 and 18.

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

How to Find the HCF of 12, 15 and 18 by Prime Factorization?

To find the HCF of 12, 15 and 18, we will find the prime factorization of given numbers, i.e. 12 = 2 × 2 × 3; 15 = 3 × 5; 18 = 2 × 3 × 3.
⇒ Since 3 is the only common prime factor of 12, 15 and 18. Hence, HCF(12, 15, 18) = 3.
☛ Prime Number