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HCF of 1001 and 385

HCF of 1001 and 385 is the largest possible number that divides 1001 and 385 exactly without any remainder. The factors of 1001 and 385 are 1, 7, 11, 13, 77, 91, 143, 1001 and 1, 5, 7, 11, 35, 55, 77, 385 respectively. There are 3 commonly used methods to find the HCF of 1001 and 385 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 1001 and 385
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 1001 and 385?

Answer: HCF of 1001 and 385 is 77.

Explanation:

The HCF of two non-zero integers, x(1001) and y(385), is the highest positive integer m(77) that divides both x(1001) and y(385) without any remainder.

Methods to Find HCF of 1001 and 385

The methods to find the HCF of 1001 and 385 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

HCF of 1001 and 385 by Prime Factorization

Prime factorization of 1001 and 385 is (7 × 11 × 13) and (5 × 7 × 11) respectively. As visible, 1001 and 385 have common prime factors. Hence, the HCF of 1001 and 385 is 7 × 11 = 77.

HCF of 1001 and 385 by Long Division

HCF of 1001 and 385 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 1001 (larger number) by 385 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (385) by the remainder (231).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (77) is the HCF of 1001 and 385.

HCF of 1001 and 385 by Listing Common Factors

Factors of 1001: 1, 7, 11, 13, 77, 91, 143, 1001
Factors of 385: 1, 5, 7, 11, 35, 55, 77, 385

There are 4 common factors of 1001 and 385, that are 1, 11, 77, and 7. Therefore, the highest common factor of 1001 and 385 is 77.

☛ Also Check:

HCF of 1001 and 385 Examples

Example 1: The product of two numbers is 385385. If their HCF is 77, what is their LCM?

Solution:

Given: HCF = 77 and product of numbers = 385385
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 385385/77
Therefore, the LCM is 5005.
Example 2: Find the highest number that divides 1001 and 385 exactly.

Solution:

The highest number that divides 1001 and 385 exactly is their highest common factor, i.e. HCF of 1001 and 385.
⇒ Factors of 1001 and 385:
- Factors of 1001 = 1, 7, 11, 13, 77, 91, 143, 1001
- Factors of 385 = 1, 5, 7, 11, 35, 55, 77, 385
Therefore, the HCF of 1001 and 385 is 77.
Example 3: For two numbers, HCF = 77 and LCM = 5005. If one number is 385, find the other number.

Solution:

Given: HCF (x, 385) = 77 and LCM (x, 385) = 5005
∵ HCF × LCM = 385 × (x)
⇒ x = (HCF × LCM)/385
⇒ x = (77 × 5005)/385
⇒ x = 1001
Therefore, the other number is 1001.

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FAQs on HCF of 1001 and 385

What is the HCF of 1001 and 385?

The HCF of 1001 and 385 is 77. To calculate the HCF (Highest Common Factor) of 1001 and 385, we need to factor each number (factors of 1001 = 1, 7, 11, 13, 77, 91, 143, 1001; factors of 385 = 1, 5, 7, 11, 35, 55, 77, 385) and choose the highest factor that exactly divides both 1001 and 385, i.e., 77.

How to Find the HCF of 1001 and 385 by Long Division Method?

To find the HCF of 1001, 385 using long division method, 1001 is divided by 385. The corresponding divisor (77) when remainder equals 0 is taken as HCF.

How to Find the HCF of 1001 and 385 by Prime Factorization?

To find the HCF of 1001 and 385, we will find the prime factorization of the given numbers, i.e. 1001 = 7 × 11 × 13; 385 = 5 × 7 × 11.
⇒ Since 7, 11 are common terms in the prime factorization of 1001 and 385. Hence, HCF(1001, 385) = 7 × 11 = 77
☛ Prime Number

If the HCF of 385 and 1001 is 77, Find its LCM.

HCF(385, 1001) × LCM(385, 1001) = 385 × 1001
Since the HCF of 385 and 1001 = 77
⇒ 77 × LCM(385, 1001) = 385385
Therefore, LCM = 5005
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What are the Methods to Find HCF of 1001 and 385?

There are three commonly used methods to find the HCF of 1001 and 385.

By Listing Common Factors
By Long Division
By Prime Factorization

What is the Relation Between LCM and HCF of 1001, 385?

The following equation can be used to express the relation between LCM and HCF of 1001 and 385, i.e. HCF × LCM = 1001 × 385.

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