Highest Common Factor of 371, 969 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 371, 969 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 371, 969 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 371, 969 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 371, 969 is 1.
HCF(371, 969) = 1
HCF of 371, 969 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 371, 969 is 1.
Highest Common Factor of 371,969 is 1
Step 1: Since 969 > 371, we apply the division lemma to 969 and 371, to get
969 = 371 x 2 + 227
Step 2: Since the reminder 371 ≠ 0, we apply division lemma to 227 and 371, to get
371 = 227 x 1 + 144
Step 3: We consider the new divisor 227 and the new remainder 144, and apply the division lemma to get
227 = 144 x 1 + 83
We consider the new divisor 144 and the new remainder 83,and apply the division lemma to get
144 = 83 x 1 + 61
We consider the new divisor 83 and the new remainder 61,and apply the division lemma to get
83 = 61 x 1 + 22
We consider the new divisor 61 and the new remainder 22,and apply the division lemma to get
61 = 22 x 2 + 17
We consider the new divisor 22 and the new remainder 17,and apply the division lemma to get
22 = 17 x 1 + 5
We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 371 and 969 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(61,22) = HCF(83,61) = HCF(144,83) = HCF(227,144) = HCF(371,227) = HCF(969,371) .
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Frequently Asked Questions on HCF of 371, 969 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 371, 969?
Answer: HCF of 371, 969 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 371, 969 using Euclid's Algorithm?
Answer: For arbitrary numbers 371, 969 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.