Highest Common Factor of 214, 508, 454 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, 508, 454 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 214, 508, 454 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 214, 508, 454 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, 508, 454 is 2.
HCF(214, 508, 454) = 2
HCF of 214, 508, 454 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, 508, 454 is 2.
Highest Common Factor of 214,508,454 is 2
Step 1: Since 508 > 214, we apply the division lemma to 508 and 214, to get
508 = 214 x 2 + 80
Step 2: Since the reminder 214 ≠ 0, we apply division lemma to 80 and 214, to get
214 = 80 x 2 + 54
Step 3: We consider the new divisor 80 and the new remainder 54, and apply the division lemma to get
80 = 54 x 1 + 26
We consider the new divisor 54 and the new remainder 26,and apply the division lemma to get
54 = 26 x 2 + 2
We consider the new divisor 26 and the new remainder 2,and apply the division lemma to get
26 = 2 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 214 and 508 is 2
Notice that 2 = HCF(26,2) = HCF(54,26) = HCF(80,54) = HCF(214,80) = HCF(508,214) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 454 > 2, we apply the division lemma to 454 and 2, to get
454 = 2 x 227 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 454 is 2
Notice that 2 = HCF(454,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 214, 508, 454 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, 508, 454?
Answer: HCF of 214, 508, 454 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 214, 508, 454 using Euclid's Algorithm?
Answer: For arbitrary numbers 214, 508, 454 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.