Highest Common Factor of 508, 778, 272 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, 778, 272 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 508, 778, 272 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 508, 778, 272 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, 778, 272 is 2.
HCF(508, 778, 272) = 2
HCF of 508, 778, 272 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, 778, 272 is 2.
Highest Common Factor of 508,778,272 is 2
Step 1: Since 778 > 508, we apply the division lemma to 778 and 508, to get
778 = 508 x 1 + 270
Step 2: Since the reminder 508 ≠ 0, we apply division lemma to 270 and 508, to get
508 = 270 x 1 + 238
Step 3: We consider the new divisor 270 and the new remainder 238, and apply the division lemma to get
270 = 238 x 1 + 32
We consider the new divisor 238 and the new remainder 32,and apply the division lemma to get
238 = 32 x 7 + 14
We consider the new divisor 32 and the new remainder 14,and apply the division lemma to get
32 = 14 x 2 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 508 and 778 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(32,14) = HCF(238,32) = HCF(270,238) = HCF(508,270) = HCF(778,508) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 272 > 2, we apply the division lemma to 272 and 2, to get
272 = 2 x 136 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 272 is 2
Notice that 2 = HCF(272,2) .
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Frequently Asked Questions on HCF of 508, 778, 272 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, 778, 272?
Answer: HCF of 508, 778, 272 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 508, 778, 272 using Euclid's Algorithm?
Answer: For arbitrary numbers 508, 778, 272 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
