Highest Common Factor of 991, 2195 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 991, 2195 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 991, 2195 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 991, 2195 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 991, 2195 is 1.
HCF(991, 2195) = 1
HCF of 991, 2195 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 991, 2195 is 1.
Highest Common Factor of 991,2195 is 1
Step 1: Since 2195 > 991, we apply the division lemma to 2195 and 991, to get
2195 = 991 x 2 + 213
Step 2: Since the reminder 991 ≠ 0, we apply division lemma to 213 and 991, to get
991 = 213 x 4 + 139
Step 3: We consider the new divisor 213 and the new remainder 139, and apply the division lemma to get
213 = 139 x 1 + 74
We consider the new divisor 139 and the new remainder 74,and apply the division lemma to get
139 = 74 x 1 + 65
We consider the new divisor 74 and the new remainder 65,and apply the division lemma to get
74 = 65 x 1 + 9
We consider the new divisor 65 and the new remainder 9,and apply the division lemma to get
65 = 9 x 7 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 991 and 2195 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(65,9) = HCF(74,65) = HCF(139,74) = HCF(213,139) = HCF(991,213) = HCF(2195,991) .
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Frequently Asked Questions on HCF of 991, 2195 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 991, 2195?
Answer: HCF of 991, 2195 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 991, 2195 using Euclid's Algorithm?
Answer: For arbitrary numbers 991, 2195 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.