Highest Common Factor of 821, 6112, 7073 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 821, 6112, 7073 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 6112, 7073 is 1 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 821, 6112, 7073 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 821, 6112, 7073 is 1.
HCF(821, 6112, 7073) = 1
HCF of 821, 6112, 7073 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 821, 6112, 7073 is 1.
Highest Common Factor of 821,6112,7073 is 1
Step 1: Since 6112 > 821, we apply the division lemma to 6112 and 821, to get
6112 = 821 x 7 + 365
Step 2: Since the reminder 821 ≠ 0, we apply division lemma to 365 and 821, to get
821 = 365 x 2 + 91
Step 3: We consider the new divisor 365 and the new remainder 91, and apply the division lemma to get
365 = 91 x 4 + 1
We consider the new divisor 91 and the new remainder 1, and apply the division lemma to get
91 = 1 x 91 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 6112 is 1
Notice that 1 = HCF(91,1) = HCF(365,91) = HCF(821,365) = HCF(6112,821) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7073 > 1, we apply the division lemma to 7073 and 1, to get
7073 = 1 x 7073 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7073 is 1
Notice that 1 = HCF(7073,1) .
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Frequently Asked Questions on HCF of 821, 6112, 7073 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 821, 6112, 7073?
Answer: HCF of 821, 6112, 7073 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 6112, 7073 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 6112, 7073 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.