Highest Common Factor of 867, 81006 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 867, 81006 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 867, 81006 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 867, 81006 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 867, 81006 is 3.
HCF(867, 81006) = 3
HCF of 867, 81006 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 867, 81006 is 3.
Highest Common Factor of 867,81006 is 3
Step 1: Since 81006 > 867, we apply the division lemma to 81006 and 867, to get
81006 = 867 x 93 + 375
Step 2: Since the reminder 867 ≠ 0, we apply division lemma to 375 and 867, to get
867 = 375 x 2 + 117
Step 3: We consider the new divisor 375 and the new remainder 117, and apply the division lemma to get
375 = 117 x 3 + 24
We consider the new divisor 117 and the new remainder 24,and apply the division lemma to get
117 = 24 x 4 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 867 and 81006 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(117,24) = HCF(375,117) = HCF(867,375) = HCF(81006,867) .
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Frequently Asked Questions on HCF of 867, 81006 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 867, 81006?
Answer: HCF of 867, 81006 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 867, 81006 using Euclid's Algorithm?
Answer: For arbitrary numbers 867, 81006 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.