Highest Common Factor of 698, 8142 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 698, 8142 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 698, 8142 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 698, 8142 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 698, 8142 is 2.
HCF(698, 8142) = 2
HCF of 698, 8142 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 698, 8142 is 2.
Highest Common Factor of 698,8142 is 2
Step 1: Since 8142 > 698, we apply the division lemma to 8142 and 698, to get
8142 = 698 x 11 + 464
Step 2: Since the reminder 698 ≠ 0, we apply division lemma to 464 and 698, to get
698 = 464 x 1 + 234
Step 3: We consider the new divisor 464 and the new remainder 234, and apply the division lemma to get
464 = 234 x 1 + 230
We consider the new divisor 234 and the new remainder 230,and apply the division lemma to get
234 = 230 x 1 + 4
We consider the new divisor 230 and the new remainder 4,and apply the division lemma to get
230 = 4 x 57 + 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 698 and 8142 is 2
Notice that 2 = HCF(4,2) = HCF(230,4) = HCF(234,230) = HCF(464,234) = HCF(698,464) = HCF(8142,698) .
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Frequently Asked Questions on HCF of 698, 8142 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 698, 8142?
Answer: HCF of 698, 8142 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 698, 8142 using Euclid's Algorithm?
Answer: For arbitrary numbers 698, 8142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
