Highest Common Factor of 528, 212, 70, 371 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, 212, 70, 371 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 528, 212, 70, 371 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 528, 212, 70, 371 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, 212, 70, 371 is 1.
HCF(528, 212, 70, 371) = 1
HCF of 528, 212, 70, 371 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, 212, 70, 371 is 1.
Highest Common Factor of 528,212,70,371 is 1
Step 1: Since 528 > 212, we apply the division lemma to 528 and 212, to get
528 = 212 x 2 + 104
Step 2: Since the reminder 212 ≠ 0, we apply division lemma to 104 and 212, to get
212 = 104 x 2 + 4
Step 3: We consider the new divisor 104 and the new remainder 4, and apply the division lemma to get
104 = 4 x 26 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 528 and 212 is 4
Notice that 4 = HCF(104,4) = HCF(212,104) = HCF(528,212) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 70 > 4, we apply the division lemma to 70 and 4, to get
70 = 4 x 17 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 70 is 2
Notice that 2 = HCF(4,2) = HCF(70,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 371 > 2, we apply the division lemma to 371 and 2, to get
371 = 2 x 185 + 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 371 is 1
Notice that 1 = HCF(2,1) = HCF(371,2) .
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Frequently Asked Questions on HCF of 528, 212, 70, 371 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, 212, 70, 371?
Answer: HCF of 528, 212, 70, 371 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 528, 212, 70, 371 using Euclid's Algorithm?
Answer: For arbitrary numbers 528, 212, 70, 371 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.