Highest Common Factor of 508, 298, 507 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 508, 298, 507 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 508, 298, 507 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 508, 298, 507 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 508, 298, 507 is 1.
HCF(508, 298, 507) = 1
HCF of 508, 298, 507 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 508, 298, 507 is 1.
Highest Common Factor of 508,298,507 is 1
Step 1: Since 508 > 298, we apply the division lemma to 508 and 298, to get
508 = 298 x 1 + 210
Step 2: Since the reminder 298 ≠ 0, we apply division lemma to 210 and 298, to get
298 = 210 x 1 + 88
Step 3: We consider the new divisor 210 and the new remainder 88, and apply the division lemma to get
210 = 88 x 2 + 34
We consider the new divisor 88 and the new remainder 34,and apply the division lemma to get
88 = 34 x 2 + 20
We consider the new divisor 34 and the new remainder 20,and apply the division lemma to get
34 = 20 x 1 + 14
We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get
20 = 14 x 1 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 508 and 298 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(34,20) = HCF(88,34) = HCF(210,88) = HCF(298,210) = HCF(508,298) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 507 > 2, we apply the division lemma to 507 and 2, to get
507 = 2 x 253 + 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 507 is 1
Notice that 1 = HCF(2,1) = HCF(507,2) .
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Frequently Asked Questions on HCF of 508, 298, 507 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 508, 298, 507?
Answer: HCF of 508, 298, 507 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 508, 298, 507 using Euclid's Algorithm?
Answer: For arbitrary numbers 508, 298, 507 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.