Highest Common Factor of 520, 200, 66 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 520, 200, 66 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 520, 200, 66 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 520, 200, 66 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 520, 200, 66 is 2.
HCF(520, 200, 66) = 2
HCF of 520, 200, 66 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 520, 200, 66 is 2.
Highest Common Factor of 520,200,66 is 2
Step 1: Since 520 > 200, we apply the division lemma to 520 and 200, to get
520 = 200 x 2 + 120
Step 2: Since the reminder 200 ≠ 0, we apply division lemma to 120 and 200, to get
200 = 120 x 1 + 80
Step 3: We consider the new divisor 120 and the new remainder 80, and apply the division lemma to get
120 = 80 x 1 + 40
We consider the new divisor 80 and the new remainder 40, and apply the division lemma to get
80 = 40 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 520 and 200 is 40
Notice that 40 = HCF(80,40) = HCF(120,80) = HCF(200,120) = HCF(520,200) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 66 > 40, we apply the division lemma to 66 and 40, to get
66 = 40 x 1 + 26
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 26 and 40, to get
40 = 26 x 1 + 14
Step 3: We consider the new divisor 26 and the new remainder 14, and apply the division lemma to get
26 = 14 x 1 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 40 and 66 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(40,26) = HCF(66,40) .
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Frequently Asked Questions on HCF of 520, 200, 66 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 520, 200, 66?
Answer: HCF of 520, 200, 66 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 520, 200, 66 using Euclid's Algorithm?
Answer: For arbitrary numbers 520, 200, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.