Highest Common Factor of 870, 681 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 870, 681 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 681 is 3 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 870, 681 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 870, 681 is 3.
HCF(870, 681) = 3
HCF of 870, 681 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 870, 681 is 3.
Highest Common Factor of 870,681 is 3
Step 1: Since 870 > 681, we apply the division lemma to 870 and 681, to get
870 = 681 x 1 + 189
Step 2: Since the reminder 681 ≠ 0, we apply division lemma to 189 and 681, to get
681 = 189 x 3 + 114
Step 3: We consider the new divisor 189 and the new remainder 114, and apply the division lemma to get
189 = 114 x 1 + 75
We consider the new divisor 114 and the new remainder 75,and apply the division lemma to get
114 = 75 x 1 + 39
We consider the new divisor 75 and the new remainder 39,and apply the division lemma to get
75 = 39 x 1 + 36
We consider the new divisor 39 and the new remainder 36,and apply the division lemma to get
39 = 36 x 1 + 3
We consider the new divisor 36 and the new remainder 3,and apply the division lemma to get
36 = 3 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 870 and 681 is 3
Notice that 3 = HCF(36,3) = HCF(39,36) = HCF(75,39) = HCF(114,75) = HCF(189,114) = HCF(681,189) = HCF(870,681) .
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Frequently Asked Questions on HCF of 870, 681 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 870, 681?
Answer: HCF of 870, 681 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 681 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 681 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.