Highest Common Factor of 8540, 698 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 8540, 698 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8540, 698 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 8540, 698 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 8540, 698 is 2.
HCF(8540, 698) = 2
HCF of 8540, 698 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8540, 698 is 2.
Highest Common Factor of 8540,698 is 2
Step 1: Since 8540 > 698, we apply the division lemma to 8540 and 698, to get
8540 = 698 x 12 + 164
Step 2: Since the reminder 698 ≠ 0, we apply division lemma to 164 and 698, to get
698 = 164 x 4 + 42
Step 3: We consider the new divisor 164 and the new remainder 42, and apply the division lemma to get
164 = 42 x 3 + 38
We consider the new divisor 42 and the new remainder 38,and apply the division lemma to get
42 = 38 x 1 + 4
We consider the new divisor 38 and the new remainder 4,and apply the division lemma to get
38 = 4 x 9 + 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 8540 and 698 is 2
Notice that 2 = HCF(4,2) = HCF(38,4) = HCF(42,38) = HCF(164,42) = HCF(698,164) = HCF(8540,698) .
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Frequently Asked Questions on HCF of 8540, 698 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 8540, 698?
Answer: HCF of 8540, 698 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8540, 698 using Euclid's Algorithm?
Answer: For arbitrary numbers 8540, 698 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.