Highest Common Factor of 688, 96210 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, 96210 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 688, 96210 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 688, 96210 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, 96210 is 2.
HCF(688, 96210) = 2
HCF of 688, 96210 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, 96210 is 2.
Highest Common Factor of 688,96210 is 2
Step 1: Since 96210 > 688, we apply the division lemma to 96210 and 688, to get
96210 = 688 x 139 + 578
Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 578 and 688, to get
688 = 578 x 1 + 110
Step 3: We consider the new divisor 578 and the new remainder 110, and apply the division lemma to get
578 = 110 x 5 + 28
We consider the new divisor 110 and the new remainder 28,and apply the division lemma to get
110 = 28 x 3 + 26
We consider the new divisor 28 and the new remainder 26,and apply the division lemma to get
28 = 26 x 1 + 2
We consider the new divisor 26 and the new remainder 2,and apply the division lemma to get
26 = 2 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 688 and 96210 is 2
Notice that 2 = HCF(26,2) = HCF(28,26) = HCF(110,28) = HCF(578,110) = HCF(688,578) = HCF(96210,688) .
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Frequently Asked Questions on HCF of 688, 96210 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, 96210?
Answer: HCF of 688, 96210 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 688, 96210 using Euclid's Algorithm?
Answer: For arbitrary numbers 688, 96210 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.