Highest Common Factor of 528, 418, 20 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 528, 418, 20 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 528, 418, 20 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 528, 418, 20 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 528, 418, 20 is 2.
HCF(528, 418, 20) = 2
HCF of 528, 418, 20 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 528, 418, 20 is 2.
Highest Common Factor of 528,418,20 is 2
Step 1: Since 528 > 418, we apply the division lemma to 528 and 418, to get
528 = 418 x 1 + 110
Step 2: Since the reminder 418 ≠ 0, we apply division lemma to 110 and 418, to get
418 = 110 x 3 + 88
Step 3: We consider the new divisor 110 and the new remainder 88, and apply the division lemma to get
110 = 88 x 1 + 22
We consider the new divisor 88 and the new remainder 22, and apply the division lemma to get
88 = 22 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 528 and 418 is 22
Notice that 22 = HCF(88,22) = HCF(110,88) = HCF(418,110) = HCF(528,418) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 22 > 20, we apply the division lemma to 22 and 20, to get
22 = 20 x 1 + 2
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 2 and 20, to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 22 and 20 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) .
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Frequently Asked Questions on HCF of 528, 418, 20 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 528, 418, 20?
Answer: HCF of 528, 418, 20 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 528, 418, 20 using Euclid's Algorithm?
Answer: For arbitrary numbers 528, 418, 20 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.