Highest Common Factor of 321, 868, 991 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 321, 868, 991 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 321, 868, 991 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 321, 868, 991 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 321, 868, 991 is 1.
HCF(321, 868, 991) = 1
HCF of 321, 868, 991 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 321, 868, 991 is 1.
Highest Common Factor of 321,868,991 is 1
Step 1: Since 868 > 321, we apply the division lemma to 868 and 321, to get
868 = 321 x 2 + 226
Step 2: Since the reminder 321 ≠ 0, we apply division lemma to 226 and 321, to get
321 = 226 x 1 + 95
Step 3: We consider the new divisor 226 and the new remainder 95, and apply the division lemma to get
226 = 95 x 2 + 36
We consider the new divisor 95 and the new remainder 36,and apply the division lemma to get
95 = 36 x 2 + 23
We consider the new divisor 36 and the new remainder 23,and apply the division lemma to get
36 = 23 x 1 + 13
We consider the new divisor 23 and the new remainder 13,and apply the division lemma to get
23 = 13 x 1 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 321 and 868 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(36,23) = HCF(95,36) = HCF(226,95) = HCF(321,226) = HCF(868,321) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 991 > 1, we apply the division lemma to 991 and 1, to get
991 = 1 x 991 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 991 is 1
Notice that 1 = HCF(991,1) .
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Frequently Asked Questions on HCF of 321, 868, 991 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 321, 868, 991?
Answer: HCF of 321, 868, 991 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 321, 868, 991 using Euclid's Algorithm?
Answer: For arbitrary numbers 321, 868, 991 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.