Highest Common Factor of 9705, 8029 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 9705, 8029 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9705, 8029 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 9705, 8029 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 9705, 8029 is 1.
HCF(9705, 8029) = 1
HCF of 9705, 8029 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9705, 8029 is 1.
Highest Common Factor of 9705,8029 is 1
Step 1: Since 9705 > 8029, we apply the division lemma to 9705 and 8029, to get
9705 = 8029 x 1 + 1676
Step 2: Since the reminder 8029 ≠ 0, we apply division lemma to 1676 and 8029, to get
8029 = 1676 x 4 + 1325
Step 3: We consider the new divisor 1676 and the new remainder 1325, and apply the division lemma to get
1676 = 1325 x 1 + 351
We consider the new divisor 1325 and the new remainder 351,and apply the division lemma to get
1325 = 351 x 3 + 272
We consider the new divisor 351 and the new remainder 272,and apply the division lemma to get
351 = 272 x 1 + 79
We consider the new divisor 272 and the new remainder 79,and apply the division lemma to get
272 = 79 x 3 + 35
We consider the new divisor 79 and the new remainder 35,and apply the division lemma to get
79 = 35 x 2 + 9
We consider the new divisor 35 and the new remainder 9,and apply the division lemma to get
35 = 9 x 3 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9705 and 8029 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(35,9) = HCF(79,35) = HCF(272,79) = HCF(351,272) = HCF(1325,351) = HCF(1676,1325) = HCF(8029,1676) = HCF(9705,8029) .
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Frequently Asked Questions on HCF of 9705, 8029 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 9705, 8029?
Answer: HCF of 9705, 8029 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9705, 8029 using Euclid's Algorithm?
Answer: For arbitrary numbers 9705, 8029 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.