Highest Common Factor of 213, 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 213, 991 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 213, 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 213, 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 213, 991 is 1.
HCF(213, 991) = 1
HCF of 213, 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 213, 991 is 1.
Highest Common Factor of 213,991 is 1
Step 1: Since 991 > 213, we apply the division lemma to 991 and 213, to get
991 = 213 x 4 + 139
Step 2: Since the reminder 213 ≠ 0, we apply division lemma to 139 and 213, to get
213 = 139 x 1 + 74
Step 3: 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 213 and 991 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) .
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Frequently Asked Questions on HCF of 213, 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 213, 991?
Answer: HCF of 213, 991 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 213, 991 using Euclid's Algorithm?
Answer: For arbitrary numbers 213, 991 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.