Highest Common Factor of 640, 20986 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 640, 20986 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 640, 20986 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 640, 20986 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 640, 20986 is 2.
HCF(640, 20986) = 2
HCF of 640, 20986 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 640, 20986 is 2.
Highest Common Factor of 640,20986 is 2
Step 1: Since 20986 > 640, we apply the division lemma to 20986 and 640, to get
20986 = 640 x 32 + 506
Step 2: Since the reminder 640 ≠ 0, we apply division lemma to 506 and 640, to get
640 = 506 x 1 + 134
Step 3: We consider the new divisor 506 and the new remainder 134, and apply the division lemma to get
506 = 134 x 3 + 104
We consider the new divisor 134 and the new remainder 104,and apply the division lemma to get
134 = 104 x 1 + 30
We consider the new divisor 104 and the new remainder 30,and apply the division lemma to get
104 = 30 x 3 + 14
We consider the new divisor 30 and the new remainder 14,and apply the division lemma to get
30 = 14 x 2 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 640 and 20986 is 2
Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(104,30) = HCF(134,104) = HCF(506,134) = HCF(640,506) = HCF(20986,640) .
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Frequently Asked Questions on HCF of 640, 20986 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 640, 20986?
Answer: HCF of 640, 20986 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 640, 20986 using Euclid's Algorithm?
Answer: For arbitrary numbers 640, 20986 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.