Highest Common Factor of 105, 441 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 105, 441 i.e. 21 the largest integer that leaves a remainder zero for all numbers.

HCF of 105, 441 is 21 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 105, 441 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 105, 441 is 21.

HCF(105, 441) = 21

HCF of 105, 441 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 105, 441 is 21.

Highest Common Factor of 105,441 using Euclid's algorithm

Highest Common Factor of 105,441 is 21

Step 1: Since 441 > 105, we apply the division lemma to 441 and 105, to get

441 = 105 x 4 + 21

Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 21 and 105, to get

105 = 21 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 105 and 441 is 21

Notice that 21 = HCF(105,21) = HCF(441,105) .

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Frequently Asked Questions on HCF of 105, 441 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 105, 441?

Answer: HCF of 105, 441 is 21 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 105, 441 using Euclid's Algorithm?

Answer: For arbitrary numbers 105, 441 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.