Highest Common Factor of 867, 640 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 867, 640 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 867, 640 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 867, 640 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 867, 640 is 1.
HCF(867, 640) = 1
HCF of 867, 640 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 867, 640 is 1.
Highest Common Factor of 867,640 is 1
Step 1: Since 867 > 640, we apply the division lemma to 867 and 640, to get
867 = 640 x 1 + 227
Step 2: Since the reminder 640 ≠ 0, we apply division lemma to 227 and 640, to get
640 = 227 x 2 + 186
Step 3: We consider the new divisor 227 and the new remainder 186, and apply the division lemma to get
227 = 186 x 1 + 41
We consider the new divisor 186 and the new remainder 41,and apply the division lemma to get
186 = 41 x 4 + 22
We consider the new divisor 41 and the new remainder 22,and apply the division lemma to get
41 = 22 x 1 + 19
We consider the new divisor 22 and the new remainder 19,and apply the division lemma to get
22 = 19 x 1 + 3
We consider the new divisor 19 and the new remainder 3,and apply the division lemma to get
19 = 3 x 6 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 867 and 640 is 1
Notice that 1 = HCF(3,1) = HCF(19,3) = HCF(22,19) = HCF(41,22) = HCF(186,41) = HCF(227,186) = HCF(640,227) = HCF(867,640) .
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Frequently Asked Questions on HCF of 867, 640 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 867, 640?
Answer: HCF of 867, 640 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 867, 640 using Euclid's Algorithm?
Answer: For arbitrary numbers 867, 640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.