Highest Common Factor of 8970, 9956, 35096 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 8970, 9956, 35096 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8970, 9956, 35096 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 8970, 9956, 35096 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 8970, 9956, 35096 is 2.
HCF(8970, 9956, 35096) = 2
HCF of 8970, 9956, 35096 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8970, 9956, 35096 is 2.
Highest Common Factor of 8970,9956,35096 is 2
Step 1: Since 9956 > 8970, we apply the division lemma to 9956 and 8970, to get
9956 = 8970 x 1 + 986
Step 2: Since the reminder 8970 ≠ 0, we apply division lemma to 986 and 8970, to get
8970 = 986 x 9 + 96
Step 3: We consider the new divisor 986 and the new remainder 96, and apply the division lemma to get
986 = 96 x 10 + 26
We consider the new divisor 96 and the new remainder 26,and apply the division lemma to get
96 = 26 x 3 + 18
We consider the new divisor 26 and the new remainder 18,and apply the division lemma to get
26 = 18 x 1 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8970 and 9956 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(26,18) = HCF(96,26) = HCF(986,96) = HCF(8970,986) = HCF(9956,8970) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 35096 > 2, we apply the division lemma to 35096 and 2, to get
35096 = 2 x 17548 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 35096 is 2
Notice that 2 = HCF(35096,2) .
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Frequently Asked Questions on HCF of 8970, 9956, 35096 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 8970, 9956, 35096?
Answer: HCF of 8970, 9956, 35096 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8970, 9956, 35096 using Euclid's Algorithm?
Answer: For arbitrary numbers 8970, 9956, 35096 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.