Highest Common Factor of 9704, 2670 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 9704, 2670 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9704, 2670 is 2 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 9704, 2670 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 9704, 2670 is 2.
HCF(9704, 2670) = 2
HCF of 9704, 2670 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9704, 2670 is 2.
Highest Common Factor of 9704,2670 is 2
Step 1: Since 9704 > 2670, we apply the division lemma to 9704 and 2670, to get
9704 = 2670 x 3 + 1694
Step 2: Since the reminder 2670 ≠ 0, we apply division lemma to 1694 and 2670, to get
2670 = 1694 x 1 + 976
Step 3: We consider the new divisor 1694 and the new remainder 976, and apply the division lemma to get
1694 = 976 x 1 + 718
We consider the new divisor 976 and the new remainder 718,and apply the division lemma to get
976 = 718 x 1 + 258
We consider the new divisor 718 and the new remainder 258,and apply the division lemma to get
718 = 258 x 2 + 202
We consider the new divisor 258 and the new remainder 202,and apply the division lemma to get
258 = 202 x 1 + 56
We consider the new divisor 202 and the new remainder 56,and apply the division lemma to get
202 = 56 x 3 + 34
We consider the new divisor 56 and the new remainder 34,and apply the division lemma to get
56 = 34 x 1 + 22
We consider the new divisor 34 and the new remainder 22,and apply the division lemma to get
34 = 22 x 1 + 12
We consider the new divisor 22 and the new remainder 12,and apply the division lemma to get
22 = 12 x 1 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9704 and 2670 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(34,22) = HCF(56,34) = HCF(202,56) = HCF(258,202) = HCF(718,258) = HCF(976,718) = HCF(1694,976) = HCF(2670,1694) = HCF(9704,2670) .
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Frequently Asked Questions on HCF of 9704, 2670 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 9704, 2670?
Answer: HCF of 9704, 2670 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9704, 2670 using Euclid's Algorithm?
Answer: For arbitrary numbers 9704, 2670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.