Highest Common Factor of 608, 8110, 9920 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 608, 8110, 9920 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 608, 8110, 9920 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 608, 8110, 9920 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 608, 8110, 9920 is 2.
HCF(608, 8110, 9920) = 2
HCF of 608, 8110, 9920 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 608, 8110, 9920 is 2.
Highest Common Factor of 608,8110,9920 is 2
Step 1: Since 8110 > 608, we apply the division lemma to 8110 and 608, to get
8110 = 608 x 13 + 206
Step 2: Since the reminder 608 ≠ 0, we apply division lemma to 206 and 608, to get
608 = 206 x 2 + 196
Step 3: We consider the new divisor 206 and the new remainder 196, and apply the division lemma to get
206 = 196 x 1 + 10
We consider the new divisor 196 and the new remainder 10,and apply the division lemma to get
196 = 10 x 19 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 608 and 8110 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(196,10) = HCF(206,196) = HCF(608,206) = HCF(8110,608) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9920 > 2, we apply the division lemma to 9920 and 2, to get
9920 = 2 x 4960 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 9920 is 2
Notice that 2 = HCF(9920,2) .
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Frequently Asked Questions on HCF of 608, 8110, 9920 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 608, 8110, 9920?
Answer: HCF of 608, 8110, 9920 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 608, 8110, 9920 using Euclid's Algorithm?
Answer: For arbitrary numbers 608, 8110, 9920 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.