HCF of 612 and 1314

HCF of 612 and 1314 is the largest possible number that divides 612 and 1314 exactly without any remainder. The factors of 612 and 1314 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612 and 1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657, 1314 respectively. There are 3 commonly used methods to find the HCF of 612 and 1314 - Euclidean algorithm, prime factorization, and long division.

Answer: HCF of 612 and 1314 is 18.

Explanation:

The HCF of two non-zero integers, x(612) and y(1314), is the highest positive integer m(18) that divides both x(612) and y(1314) without any remainder.

Let's look at the different methods for finding the HCF of 612 and 1314.

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

HCF of 612 and 1314 by Prime Factorization

Prime factorization of 612 and 1314 is (2 × 2 × 3 × 3 × 17) and (2 × 3 × 3 × 73) respectively. As visible, 612 and 1314 have common prime factors. Hence, the HCF of 612 and 1314 is 2 × 3 × 3 = 18.

HCF of 612 and 1314 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 = 1314 and Y = 612

• HCF(1314, 612) = HCF(612, 1314 mod 612) = HCF(612, 90)
• HCF(612, 90) = HCF(90, 612 mod 90) = HCF(90, 72)
• HCF(90, 72) = HCF(72, 90 mod 72) = HCF(72, 18)
• HCF(72, 18) = HCF(18, 72 mod 18) = HCF(18, 0)
• HCF(18, 0) = 18 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 612 and 1314 is 18.

HCF of 612 and 1314 by Long Division

HCF of 612 and 1314 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 1314 (larger number) by 612 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (612) by the remainder (90).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (18) is the HCF of 612 and 1314.

☛ Also Check:

• HCF of 18 and 24 = 6
• HCF of 510 and 92 = 2
• HCF of 18 and 45 = 9
• HCF of 36 and 48 = 12
• HCF of 12 and 20 = 4
• HCF of 100 and 190 = 10
• HCF of 336 and 54 = 6

FAQs on HCF of 612 and 1314

What is the HCF of 612 and 1314?

The HCF of 612 and 1314 is 18. To calculate the HCF (Highest Common Factor) of 612 and 1314, we need to factor each number (factors of 612 = 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612; factors of 1314 = 1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657, 1314) and choose the highest factor that exactly divides both 612 and 1314, i.e., 18.

What is the Relation Between LCM and HCF of 612, 1314?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 612 and 1314, i.e. HCF × LCM = 612 × 1314.

How to Find the HCF of 612 and 1314 by Prime Factorization?

To find the HCF of 612 and 1314, we will find the prime factorization of the given numbers, i.e. 612 = 2 × 2 × 3 × 3 × 17; 1314 = 2 × 3 × 3 × 73.
⇒ Since 2, 3, 3 are common terms in the prime factorization of 612 and 1314. Hence, HCF(612, 1314) = 2 × 3 × 3 = 18
☛ Prime Number

If the HCF of 1314 and 612 is 18, Find its LCM.

HCF(1314, 612) × LCM(1314, 612) = 1314 × 612
Since the HCF of 1314 and 612 = 18
⇒ 18 × LCM(1314, 612) = 804168
Therefore, LCM = 44676
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 612 and 1314?

There are three commonly used methods to find the HCF of 612 and 1314.

• By Long Division
• By Listing Common Factors
• By Prime Factorization

How to Find the HCF of 612 and 1314 by Long Division Method?

To find the HCF of 612, 1314 using long division method, 1314 is divided by 612. The corresponding divisor (18) when remainder equals 0 is taken as HCF.