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HCF of 513, 1134 and 1215

HCF of 513, 1134 and 1215 is the largest possible number that divides 513, 1134 and 1215 exactly without any remainder. The factors of 513, 1134 and 1215 are (1, 3, 9, 19, 27, 57, 171, 513), (1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 378, 567, 1134) and (1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215) respectively. There are 3 commonly used methods to find the HCF of 513, 1134 and 1215 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 513, 1134 and 1215
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 513, 1134 and 1215?

Answer: HCF of 513, 1134 and 1215 is 27.

Explanation:

The HCF of three non-zero integers, x(513), y(1134) and z(1215), is the highest positive integer m(27) that divides x(513), y(1134) and z(1215) without any remainder.

Methods to Find HCF of 513, 1134 and 1215

Let's look at the different methods for finding the HCF of 513, 1134 and 1215.

Long Division Method
Listing Common Factors
Prime Factorization Method

HCF of 513, 1134 and 1215 by Long Division

HCF of 513, 1134 and 1215 can be represented as HCF of (HCF of 513, 1134) and 1215. HCF(513, 1134, 1215) can be thus calculated by first finding HCF(513, 1134) using long division and thereafter using this result with 1215 to perform long division again.

Step 1: Divide 1134 (larger number) by 513 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (513) by the remainder (108). Repeat this process until the remainder = 0.
⇒ HCF(513, 1134) = 27.
Step 3: Now to find the HCF of 27 and 1215, we will perform a long division on 1215 and 27.
Step 4: For remainder = 0, divisor = 27 ⇒ HCF(27, 1215) = 27

Thus, HCF(513, 1134, 1215) = HCF(HCF(513, 1134), 1215) = 27.

HCF of 513, 1134 and 1215 by Listing Common Factors

Factors of 513: 1, 3, 9, 19, 27, 57, 171, 513
Factors of 1134: 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 378, 567, 1134
Factors of 1215: 1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215

There are 4 common factors of 513, 1134 and 1215, that are 3, 1, 27, and 9. Therefore, the highest common factor of 513, 1134 and 1215 is 27.

HCF of 513, 1134 and 1215 by Prime Factorization

Prime factorization of 513, 1134 and 1215 is (3 × 3 × 3 × 19), (2 × 3 × 3 × 3 × 3 × 7) and (3 × 3 × 3 × 3 × 3 × 5) respectively. As visible, 513, 1134 and 1215 have common prime factors. Hence, the HCF of 513, 1134 and 1215 is 3 × 3 × 3 = 27.

☛ Also Check:

HCF of 513, 1134 and 1215 Examples

Example 1: Calculate the HCF of 513, 1134, and 1215 using LCM of the given numbers.

Solution:

Prime factorization of 513, 1134 and 1215 is given as,
- 513 = 3 × 3 × 3 × 19
- 1134 = 2 × 3 × 3 × 3 × 3 × 7
- 1215 = 3 × 3 × 3 × 3 × 3 × 5
LCM(513, 1134) = 21546, LCM(1134, 1215) = 17010, LCM(1215, 513) = 23085, LCM(513, 1134, 1215) = 323190
⇒ HCF(513, 1134, 1215) = [(513 × 1134 × 1215) × LCM(513, 1134, 1215)]/[LCM(513, 1134) × LCM (1134, 1215) × LCM(1215, 513)]
⇒ HCF(513, 1134, 1215) = (706816530 × 323190)/(21546 × 17010 × 23085)
⇒ HCF(513, 1134, 1215) = 27.
Therefore, the HCF of 513, 1134 and 1215 is 27.
Example 2: Find the highest number that divides 513, 1134, and 1215 completely.

Solution:

The highest number that divides 513, 1134, and 1215 exactly is their highest common factor.
- Factors of 513 = 1, 3, 9, 19, 27, 57, 171, 513
- Factors of 1134 = 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 378, 567, 1134
- Factors of 1215 = 1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215
The HCF of 513, 1134, and 1215 is 27.
∴ The highest number that divides 513, 1134, and 1215 is 27.
Example 3: Verify the relation between the LCM and HCF of 513, 1134 and 1215.

Solution:

The relation between the LCM and HCF of 513, 1134 and 1215 is given as, HCF(513, 1134, 1215) = [(513 × 1134 × 1215) × LCM(513, 1134, 1215)]/[LCM(513, 1134) × LCM (1134, 1215) × LCM(513, 1215)]
⇒ Prime factorization of 513, 1134 and 1215:
- 513 = 3 × 3 × 3 × 19
- 1134 = 2 × 3 × 3 × 3 × 3 × 7
- 1215 = 3 × 3 × 3 × 3 × 3 × 5
∴ LCM of (513, 1134), (1134, 1215), (513, 1215), and (513, 1134, 1215) is 21546, 17010, 23085, and 323190 respectively.
Now, LHS = HCF(513, 1134, 1215) = 27.
And, RHS = [(513 × 1134 × 1215) × LCM(513, 1134, 1215)]/[LCM(513, 1134) × LCM (1134, 1215) × LCM(513, 1215)] = [(706816530) × 323190]/[21546 × 17010 × 23085]
LHS = RHS = 27.
Hence verified.

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FAQs on HCF of 513, 1134 and 1215

What is the HCF of 513, 1134 and 1215?

The HCF of 513, 1134 and 1215 is 27. To calculate the highest common factor of 513, 1134 and 1215, we need to factor each number (factors of 513 = 1, 3, 9, 19, 27, 57, 171, 513; factors of 1134 = 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 378, 567, 1134; factors of 1215 = 1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215) and choose the highest factor that exactly divides 513, 1134 and 1215, i.e., 27.

How to Find the HCF of 513, 1134 and 1215 by Prime Factorization?

To find the HCF of 513, 1134 and 1215, we will find the prime factorization of given numbers, i.e. 513 = 3 × 3 × 3 × 19; 1134 = 2 × 3 × 3 × 3 × 3 × 7; 1215 = 3 × 3 × 3 × 3 × 3 × 5.
⇒ Since 3, 3, 3 are common terms in the prime factorization of 513, 1134 and 1215. Hence, HCF(513, 1134, 1215) = 3 × 3 × 3 = 27
☛ Prime Numbers

What are the Methods to Find HCF of 513, 1134 and 1215?

There are three commonly used methods to find the HCF of 513, 1134 and 1215.

By Euclidean Algorithm
By Long Division
By Prime Factorization

Which of the following is HCF of 513, 1134 and 1215? 27, 1243, 1235, 1250, 1245, 1243, 1225

HCF of 513, 1134, 1215 will be the number that divides 513, 1134, and 1215 without leaving any remainder. The only number that satisfies the given condition is 27.

What is the Relation Between LCM and HCF of 513, 1134 and 1215?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 513, 1134 and 1215, i.e. HCF(513, 1134, 1215) = [(513 × 1134 × 1215) × LCM(513, 1134, 1215)]/[LCM(513, 1134) × LCM (1134, 1215) × LCM(513, 1215)].
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