Highest Common Factor of 7923, 8166 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 7923, 8166 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 7923, 8166 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 7923, 8166 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 7923, 8166 is 3.
HCF(7923, 8166) = 3
HCF of 7923, 8166 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7923, 8166 is 3.
Highest Common Factor of 7923,8166 is 3
Step 1: Since 8166 > 7923, we apply the division lemma to 8166 and 7923, to get
8166 = 7923 x 1 + 243
Step 2: Since the reminder 7923 ≠ 0, we apply division lemma to 243 and 7923, to get
7923 = 243 x 32 + 147
Step 3: We consider the new divisor 243 and the new remainder 147, and apply the division lemma to get
243 = 147 x 1 + 96
We consider the new divisor 147 and the new remainder 96,and apply the division lemma to get
147 = 96 x 1 + 51
We consider the new divisor 96 and the new remainder 51,and apply the division lemma to get
96 = 51 x 1 + 45
We consider the new divisor 51 and the new remainder 45,and apply the division lemma to get
51 = 45 x 1 + 6
We consider the new divisor 45 and the new remainder 6,and apply the division lemma to get
45 = 6 x 7 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 7923 and 8166 is 3
Notice that 3 = HCF(6,3) = HCF(45,6) = HCF(51,45) = HCF(96,51) = HCF(147,96) = HCF(243,147) = HCF(7923,243) = HCF(8166,7923) .
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Frequently Asked Questions on HCF of 7923, 8166 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 7923, 8166?
Answer: HCF of 7923, 8166 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7923, 8166 using Euclid's Algorithm?
Answer: For arbitrary numbers 7923, 8166 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.