Highest Common Factor of 862, 960, 641 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 862, 960, 641 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 862, 960, 641 is 1 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 862, 960, 641 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 862, 960, 641 is 1.
HCF(862, 960, 641) = 1
HCF of 862, 960, 641 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 862, 960, 641 is 1.
Highest Common Factor of 862,960,641 is 1
Step 1: Since 960 > 862, we apply the division lemma to 960 and 862, to get
960 = 862 x 1 + 98
Step 2: Since the reminder 862 ≠ 0, we apply division lemma to 98 and 862, to get
862 = 98 x 8 + 78
Step 3: We consider the new divisor 98 and the new remainder 78, and apply the division lemma to get
98 = 78 x 1 + 20
We consider the new divisor 78 and the new remainder 20,and apply the division lemma to get
78 = 20 x 3 + 18
We consider the new divisor 20 and the new remainder 18,and apply the division lemma to get
20 = 18 x 1 + 2
We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 862 and 960 is 2
Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(78,20) = HCF(98,78) = HCF(862,98) = HCF(960,862) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 641 > 2, we apply the division lemma to 641 and 2, to get
641 = 2 x 320 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 641 is 1
Notice that 1 = HCF(2,1) = HCF(641,2) .
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Frequently Asked Questions on HCF of 862, 960, 641 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 862, 960, 641?
Answer: HCF of 862, 960, 641 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 862, 960, 641 using Euclid's Algorithm?
Answer: For arbitrary numbers 862, 960, 641 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
