Highest Common Factor of 8106, 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 8106, 969 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8106, 969 is 3 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 8106, 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 8106, 969 is 3.
HCF(8106, 969) = 3
HCF of 8106, 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 8106, 969 is 3.
Highest Common Factor of 8106,969 is 3
Step 1: Since 8106 > 969, we apply the division lemma to 8106 and 969, to get
8106 = 969 x 8 + 354
Step 2: Since the reminder 969 ≠ 0, we apply division lemma to 354 and 969, to get
969 = 354 x 2 + 261
Step 3: We consider the new divisor 354 and the new remainder 261, and apply the division lemma to get
354 = 261 x 1 + 93
We consider the new divisor 261 and the new remainder 93,and apply the division lemma to get
261 = 93 x 2 + 75
We consider the new divisor 93 and the new remainder 75,and apply the division lemma to get
93 = 75 x 1 + 18
We consider the new divisor 75 and the new remainder 18,and apply the division lemma to get
75 = 18 x 4 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8106 and 969 is 3
Notice that 3 = HCF(18,3) = HCF(75,18) = HCF(93,75) = HCF(261,93) = HCF(354,261) = HCF(969,354) = HCF(8106,969) .
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Frequently Asked Questions on HCF of 8106, 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 8106, 969?
Answer: HCF of 8106, 969 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8106, 969 using Euclid's Algorithm?
Answer: For arbitrary numbers 8106, 969 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.