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HCF of 1517 and 902

HCF of 1517 and 902 is the largest possible number that divides 1517 and 902 exactly without any remainder. The factors of 1517 and 902 are 1, 37, 41, 1517 and 1, 2, 11, 22, 41, 82, 451, 902 respectively. There are 3 commonly used methods to find the HCF of 1517 and 902 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 1517 and 902
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 1517 and 902?

Answer: HCF of 1517 and 902 is 41.

Explanation:

The HCF of two non-zero integers, x(1517) and y(902), is the highest positive integer m(41) that divides both x(1517) and y(902) without any remainder.

Methods to Find HCF of 1517 and 902

Let's look at the different methods for finding the HCF of 1517 and 902.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

HCF of 1517 and 902 by Long Division

HCF of 1517 and 902 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 1517 (larger number) by 902 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (902) by the remainder (615).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (41) is the HCF of 1517 and 902.

HCF of 1517 and 902 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 = 1517 and Y = 902

HCF(1517, 902) = HCF(902, 1517 mod 902) = HCF(902, 615)
HCF(902, 615) = HCF(615, 902 mod 615) = HCF(615, 287)
HCF(615, 287) = HCF(287, 615 mod 287) = HCF(287, 41)
HCF(287, 41) = HCF(41, 287 mod 41) = HCF(41, 0)
HCF(41, 0) = 41 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 1517 and 902 is 41.

HCF of 1517 and 902 by Listing Common Factors

Factors of 1517: 1, 37, 41, 1517
Factors of 902: 1, 2, 11, 22, 41, 82, 451, 902

There are 2 common factors of 1517 and 902, that are 1 and 41. Therefore, the highest common factor of 1517 and 902 is 41.

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HCF of 1517 and 902 Examples

Example 1: Find the highest number that divides 1517 and 902 exactly.

Solution:

The highest number that divides 1517 and 902 exactly is their highest common factor, i.e. HCF of 1517 and 902.
⇒ Factors of 1517 and 902:
- Factors of 1517 = 1, 37, 41, 1517
- Factors of 902 = 1, 2, 11, 22, 41, 82, 451, 902
Therefore, the HCF of 1517 and 902 is 41.
Example 2: For two numbers, HCF = 41 and LCM = 33374. If one number is 902, find the other number.

Solution:

Given: HCF (z, 902) = 41 and LCM (z, 902) = 33374
∵ HCF × LCM = 902 × (z)
⇒ z = (HCF × LCM)/902
⇒ z = (41 × 33374)/902
⇒ z = 1517
Therefore, the other number is 1517.
Example 3: Find the HCF of 1517 and 902, if their LCM is 33374.

Solution:

∵ LCM × HCF = 1517 × 902
⇒ HCF(1517, 902) = (1517 × 902)/33374 = 41
Therefore, the highest common factor of 1517 and 902 is 41.

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FAQs on HCF of 1517 and 902

What is the HCF of 1517 and 902?

The HCF of 1517 and 902 is 41. To calculate the HCF of 1517 and 902, we need to factor each number (factors of 1517 = 1, 37, 41, 1517; factors of 902 = 1, 2, 11, 22, 41, 82, 451, 902) and choose the highest factor that exactly divides both 1517 and 902, i.e., 41.

How to Find the HCF of 1517 and 902 by Long Division Method?

To find the HCF of 1517, 902 using long division method, 1517 is divided by 902. The corresponding divisor (41) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 1517 and 902?

There are three commonly used methods to find the HCF of 1517 and 902.

By Euclidean Algorithm
By Long Division
By Prime Factorization

How to Find the HCF of 1517 and 902 by Prime Factorization?

To find the HCF of 1517 and 902, we will find the prime factorization of the given numbers, i.e. 1517 = 37 × 41; 902 = 2 × 11 × 41.
⇒ Since 41 is the only common prime factor of 1517 and 902. Hence, HCF (1517, 902) = 41.
☛ What are Prime Numbers?

What is the Relation Between LCM and HCF of 1517, 902?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 1517 and 902, i.e. HCF × LCM = 1517 × 902.

If the HCF of 902 and 1517 is 41, Find its LCM.

HCF(902, 1517) × LCM(902, 1517) = 902 × 1517
Since the HCF of 902 and 1517 = 41
⇒ 41 × LCM(902, 1517) = 1368334
Therefore, LCM = 33374
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