Highest Common Factor of 973, 8136 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 973, 8136 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 973, 8136 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 973, 8136 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 973, 8136 is 1.
HCF(973, 8136) = 1
HCF of 973, 8136 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 973, 8136 is 1.
Highest Common Factor of 973,8136 is 1
Step 1: Since 8136 > 973, we apply the division lemma to 8136 and 973, to get
8136 = 973 x 8 + 352
Step 2: Since the reminder 973 ≠ 0, we apply division lemma to 352 and 973, to get
973 = 352 x 2 + 269
Step 3: We consider the new divisor 352 and the new remainder 269, and apply the division lemma to get
352 = 269 x 1 + 83
We consider the new divisor 269 and the new remainder 83,and apply the division lemma to get
269 = 83 x 3 + 20
We consider the new divisor 83 and the new remainder 20,and apply the division lemma to get
83 = 20 x 4 + 3
We consider the new divisor 20 and the new remainder 3,and apply the division lemma to get
20 = 3 x 6 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 973 and 8136 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(83,20) = HCF(269,83) = HCF(352,269) = HCF(973,352) = HCF(8136,973) .
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Frequently Asked Questions on HCF of 973, 8136 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 973, 8136?
Answer: HCF of 973, 8136 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 973, 8136 using Euclid's Algorithm?
Answer: For arbitrary numbers 973, 8136 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
