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HCF of 1001 and 910

HCF of 1001 and 910 is the largest possible number that divides 1001 and 910 exactly without any remainder. The factors of 1001 and 910 are 1, 7, 11, 13, 77, 91, 143, 1001 and 1, 2, 5, 7, 10, 13, 14, 26, 35, 65, 70, 91, 130, 182, 455, 910 respectively. There are 3 commonly used methods to find the HCF of 1001 and 910 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 1001 and 910
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 1001 and 910?

Answer: HCF of 1001 and 910 is 91.

Explanation:

The HCF of two non-zero integers, x(1001) and y(910), is the highest positive integer m(91) that divides both x(1001) and y(910) without any remainder.

Methods to Find HCF of 1001 and 910

The methods to find the HCF of 1001 and 910 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

HCF of 1001 and 910 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 = 1001 and Y = 910

HCF(1001, 910) = HCF(910, 1001 mod 910) = HCF(910, 91)
HCF(910, 91) = HCF(91, 910 mod 91) = HCF(91, 0)
HCF(91, 0) = 91 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 1001 and 910 is 91.

HCF of 1001 and 910 by Long Division

HCF of 1001 and 910 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 1001 (larger number) by 910 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (910) by the remainder (91).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (91) is the HCF of 1001 and 910.

HCF of 1001 and 910 by Listing Common Factors

Factors of 1001: 1, 7, 11, 13, 77, 91, 143, 1001
Factors of 910: 1, 2, 5, 7, 10, 13, 14, 26, 35, 65, 70, 91, 130, 182, 455, 910

There are 4 common factors of 1001 and 910, that are 1, 91, 13, and 7. Therefore, the highest common factor of 1001 and 910 is 91.

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HCF of 1001 and 910 Examples

Example 1: For two numbers, HCF = 91 and LCM = 10010. If one number is 1001, find the other number.

Solution:

Given: HCF (z, 1001) = 91 and LCM (z, 1001) = 10010
∵ HCF × LCM = 1001 × (z)
⇒ z = (HCF × LCM)/1001
⇒ z = (91 × 10010)/1001
⇒ z = 910
Therefore, the other number is 910.
Example 2: The product of two numbers is 910910. If their HCF is 91, what is their LCM?

Solution:

Given: HCF = 91 and product of numbers = 910910
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 910910/91
Therefore, the LCM is 10010.
Example 3: Find the highest number that divides 1001 and 910 exactly.

Solution:

The highest number that divides 1001 and 910 exactly is their highest common factor, i.e. HCF of 1001 and 910.
⇒ Factors of 1001 and 910:
- Factors of 1001 = 1, 7, 11, 13, 77, 91, 143, 1001
- Factors of 910 = 1, 2, 5, 7, 10, 13, 14, 26, 35, 65, 70, 91, 130, 182, 455, 910
Therefore, the HCF of 1001 and 910 is 91.

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FAQs on HCF of 1001 and 910

What is the HCF of 1001 and 910?

The HCF of 1001 and 910 is 91. To calculate the Highest common factor of 1001 and 910, we need to factor each number (factors of 1001 = 1, 7, 11, 13, 77, 91, 143, 1001; factors of 910 = 1, 2, 5, 7, 10, 13, 14, 26, 35, 65, 70, 91, 130, 182, 455, 910) and choose the highest factor that exactly divides both 1001 and 910, i.e., 91.

How to Find the HCF of 1001 and 910 by Long Division Method?

To find the HCF of 1001, 910 using long division method, 1001 is divided by 910. The corresponding divisor (91) when remainder equals 0 is taken as HCF.

If the HCF of 910 and 1001 is 91, Find its LCM.

HCF(910, 1001) × LCM(910, 1001) = 910 × 1001
Since the HCF of 910 and 1001 = 91
⇒ 91 × LCM(910, 1001) = 910910
Therefore, LCM = 10010
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What are the Methods to Find HCF of 1001 and 910?

There are three commonly used methods to find the HCF of 1001 and 910.

By Long Division
By Listing Common Factors
By Prime Factorization

What is the Relation Between LCM and HCF of 1001, 910?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 1001 and 910, i.e. HCF × LCM = 1001 × 910.

How to Find the HCF of 1001 and 910 by Prime Factorization?

To find the HCF of 1001 and 910, we will find the prime factorization of the given numbers, i.e. 1001 = 7 × 11 × 13; 910 = 2 × 5 × 7 × 13.
⇒ Since 7, 13 are common terms in the prime factorization of 1001 and 910. Hence, HCF(1001, 910) = 7 × 13 = 91
☛ What is a Prime Number?

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