Highest Common Factor of 214, 750, 471 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 214, 750, 471 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 214, 750, 471 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 214, 750, 471 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 214, 750, 471 is 1.
HCF(214, 750, 471) = 1
HCF of 214, 750, 471 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 214, 750, 471 is 1.
Highest Common Factor of 214,750,471 is 1
Step 1: Since 750 > 214, we apply the division lemma to 750 and 214, to get
750 = 214 x 3 + 108
Step 2: Since the reminder 214 ≠ 0, we apply division lemma to 108 and 214, to get
214 = 108 x 1 + 106
Step 3: We consider the new divisor 108 and the new remainder 106, and apply the division lemma to get
108 = 106 x 1 + 2
We consider the new divisor 106 and the new remainder 2, and apply the division lemma to get
106 = 2 x 53 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 214 and 750 is 2
Notice that 2 = HCF(106,2) = HCF(108,106) = HCF(214,108) = HCF(750,214) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 471 > 2, we apply the division lemma to 471 and 2, to get
471 = 2 x 235 + 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 471 is 1
Notice that 1 = HCF(2,1) = HCF(471,2) .
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Frequently Asked Questions on HCF of 214, 750, 471 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 214, 750, 471?
Answer: HCF of 214, 750, 471 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 214, 750, 471 using Euclid's Algorithm?
Answer: For arbitrary numbers 214, 750, 471 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.