Highest Common Factor of 688, 86989 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 688, 86989 i.e. 43 the largest integer that leaves a remainder zero for all numbers.
HCF of 688, 86989 is 43 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 688, 86989 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 688, 86989 is 43.
HCF(688, 86989) = 43
HCF of 688, 86989 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 688, 86989 is 43.
Highest Common Factor of 688,86989 is 43
Step 1: Since 86989 > 688, we apply the division lemma to 86989 and 688, to get
86989 = 688 x 126 + 301
Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 301 and 688, to get
688 = 301 x 2 + 86
Step 3: We consider the new divisor 301 and the new remainder 86, and apply the division lemma to get
301 = 86 x 3 + 43
We consider the new divisor 86 and the new remainder 43, and apply the division lemma to get
86 = 43 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 43, the HCF of 688 and 86989 is 43
Notice that 43 = HCF(86,43) = HCF(301,86) = HCF(688,301) = HCF(86989,688) .
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Frequently Asked Questions on HCF of 688, 86989 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 688, 86989?
Answer: HCF of 688, 86989 is 43 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 688, 86989 using Euclid's Algorithm?
Answer: For arbitrary numbers 688, 86989 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.