Highest Common Factor of 821, 629, 892, 165 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, 629, 892, 165 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 629, 892, 165 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, 629, 892, 165 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, 629, 892, 165 is 1.
HCF(821, 629, 892, 165) = 1
HCF of 821, 629, 892, 165 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, 629, 892, 165 is 1.
Highest Common Factor of 821,629,892,165 is 1
Step 1: Since 821 > 629, we apply the division lemma to 821 and 629, to get
821 = 629 x 1 + 192
Step 2: Since the reminder 629 ≠ 0, we apply division lemma to 192 and 629, to get
629 = 192 x 3 + 53
Step 3: We consider the new divisor 192 and the new remainder 53, and apply the division lemma to get
192 = 53 x 3 + 33
We consider the new divisor 53 and the new remainder 33,and apply the division lemma to get
53 = 33 x 1 + 20
We consider the new divisor 33 and the new remainder 20,and apply the division lemma to get
33 = 20 x 1 + 13
We consider the new divisor 20 and the new remainder 13,and apply the division lemma to get
20 = 13 x 1 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 629 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(20,13) = HCF(33,20) = HCF(53,33) = HCF(192,53) = HCF(629,192) = HCF(821,629) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 892 > 1, we apply the division lemma to 892 and 1, to get
892 = 1 x 892 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 892 is 1
Notice that 1 = HCF(892,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 165 > 1, we apply the division lemma to 165 and 1, to get
165 = 1 x 165 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 165 is 1
Notice that 1 = HCF(165,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 821, 629, 892, 165 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, 629, 892, 165?
Answer: HCF of 821, 629, 892, 165 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 629, 892, 165 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 629, 892, 165 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.