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HCF of 204, 1190 and 1445

HCF of 204, 1190 and 1445 is the largest possible number that divides 204, 1190 and 1445 exactly without any remainder. The factors of 204, 1190 and 1445 are (1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204), (1, 2, 5, 7, 10, 14, 17, 34, 35, 70, 85, 119, 170, 238, 595, 1190) and (1, 5, 17, 85, 289, 1445) respectively. There are 3 commonly used methods to find the HCF of 204, 1190 and 1445 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 204, 1190 and 1445
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 204, 1190 and 1445?

Answer: HCF of 204, 1190 and 1445 is 17.

Explanation:

The HCF of three non-zero integers, x(204), y(1190) and z(1445), is the highest positive integer m(17) that divides x(204), y(1190) and z(1445) without any remainder.

Methods to Find HCF of 204, 1190 and 1445

Let's look at the different methods for finding the HCF of 204, 1190 and 1445.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

HCF of 204, 1190 and 1445 by Long Division

HCF of 204, 1190 and 1445 can be represented as HCF of (HCF of 204, 1190) and 1445. HCF(204, 1190, 1445) can be thus calculated by first finding HCF(204, 1190) using long division and thereafter using this result with 1445 to perform long division again.

Step 1: Divide 1190 (larger number) by 204 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (204) by the remainder (170). Repeat this process until the remainder = 0.
⇒ HCF(204, 1190) = 34.
Step 3: Now to find the HCF of 34 and 1445, we will perform a long division on 1445 and 34.
Step 4: For remainder = 0, divisor = 17 ⇒ HCF(34, 1445) = 17

Thus, HCF(204, 1190, 1445) = HCF(HCF(204, 1190), 1445) = 17.

HCF of 204, 1190 and 1445 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(204, 1190, 1445) = HCF(HCF(204, 1190), 1445)

HCF(1190, 204) = HCF(204, 1190 mod 204) = HCF(204, 170)
HCF(204, 170) = HCF(170, 204 mod 170) = HCF(170, 34)
HCF(170, 34) = HCF(34, 170 mod 34) = HCF(34, 0)
HCF(34, 0) = 34 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Steps for HCF(34, 1445)

HCF(1445, 34) = HCF(34, 1445 mod 34) = HCF(34, 17)
HCF(34, 17) = HCF(17, 34 mod 17) = HCF(17, 0)
HCF(17, 0) = 17 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 204, 1190 and 1445 is 17.

HCF of 204, 1190 and 1445 by Prime Factorization

Prime factorization of 204, 1190 and 1445 is (2 × 2 × 3 × 17), (2 × 5 × 7 × 17) and (5 × 17 × 17) respectively. As visible, 204, 1190 and 1445 have only one common prime factor i.e. 17. Hence, the HCF of 204, 1190 and 1445 is 17.

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HCF of 204, 1190 and 1445 Examples

Example 1: Find the highest number that divides 204, 1190, and 1445 completely.

Solution:

The highest number that divides 204, 1190, and 1445 exactly is their highest common factor.
- Factors of 204 = 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
- Factors of 1190 = 1, 2, 5, 7, 10, 14, 17, 34, 35, 70, 85, 119, 170, 238, 595, 1190
- Factors of 1445 = 1, 5, 17, 85, 289, 1445
The HCF of 204, 1190, and 1445 is 17.
∴ The highest number that divides 204, 1190, and 1445 is 17.
Example 2: Verify the relation between the LCM and HCF of 204, 1190 and 1445.

Solution:

The relation between the LCM and HCF of 204, 1190 and 1445 is given as, HCF(204, 1190, 1445) = [(204 × 1190 × 1445) × LCM(204, 1190, 1445)]/[LCM(204, 1190) × LCM (1190, 1445) × LCM(204, 1445)]
⇒ Prime factorization of 204, 1190 and 1445:
- 204 = 2 × 2 × 3 × 17
- 1190 = 2 × 5 × 7 × 17
- 1445 = 5 × 17 × 17
∴ LCM of (204, 1190), (1190, 1445), (204, 1445), and (204, 1190, 1445) is 7140, 20230, 17340, and 121380 respectively.
Now, LHS = HCF(204, 1190, 1445) = 17.
And, RHS = [(204 × 1190 × 1445) × LCM(204, 1190, 1445)]/[LCM(204, 1190) × LCM (1190, 1445) × LCM(204, 1445)] = [(350788200) × 121380]/[7140 × 20230 × 17340]
LHS = RHS = 17.
Hence verified.
Example 3: Calculate the HCF of 204, 1190, and 1445 using LCM of the given numbers.

Solution:

Prime factorization of 204, 1190 and 1445 is given as,
- 204 = 2 × 2 × 3 × 17
- 1190 = 2 × 5 × 7 × 17
- 1445 = 5 × 17 × 17
LCM(204, 1190) = 7140, LCM(1190, 1445) = 20230, LCM(1445, 204) = 17340, LCM(204, 1190, 1445) = 121380
⇒ HCF(204, 1190, 1445) = [(204 × 1190 × 1445) × LCM(204, 1190, 1445)]/[LCM(204, 1190) × LCM (1190, 1445) × LCM(1445, 204)]
⇒ HCF(204, 1190, 1445) = (350788200 × 121380)/(7140 × 20230 × 17340)
⇒ HCF(204, 1190, 1445) = 17.
Therefore, the HCF of 204, 1190 and 1445 is 17.

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FAQs on HCF of 204, 1190 and 1445

What is the HCF of 204, 1190 and 1445?

The HCF of 204, 1190 and 1445 is 17. To calculate the HCF (Highest Common Factor) of 204, 1190 and 1445, we need to factor each number (factors of 204 = 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204; factors of 1190 = 1, 2, 5, 7, 10, 14, 17, 34, 35, 70, 85, 119, 170, 238, 595, 1190; factors of 1445 = 1, 5, 17, 85, 289, 1445) and choose the highest factor that exactly divides 204, 1190 and 1445, i.e., 17.

How to Find the HCF of 204, 1190 and 1445 by Prime Factorization?

To find the HCF of 204, 1190 and 1445, we will find the prime factorization of given numbers, i.e. 204 = 2 × 2 × 3 × 17; 1190 = 2 × 5 × 7 × 17; 1445 = 5 × 17 × 17.
⇒ Since 17 is the only common prime factor of 204, 1190 and 1445. Hence, HCF(204, 1190, 1445) = 17.
☛ Prime Number

What is the Relation Between LCM and HCF of 204, 1190 and 1445?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 204, 1190 and 1445, i.e. HCF(204, 1190, 1445) = [(204 × 1190 × 1445) × LCM(204, 1190, 1445)]/[LCM(204, 1190) × LCM (1190, 1445) × LCM(204, 1445)].
☛ HCF Calculator

Which of the following is HCF of 204, 1190 and 1445? 17, 1451, 1478, 1487, 1493, 1491, 1467, 1481, 1466

HCF of 204, 1190, 1445 will be the number that divides 204, 1190, and 1445 without leaving any remainder. The only number that satisfies the given condition is 17.

What are the Methods to Find HCF of 204, 1190 and 1445?

There are three commonly used methods to find the HCF of 204, 1190 and 1445.

By Prime Factorization
By Listing Common Factors
By Long Division

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