Highest Common Factor of 510, 782, 164 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 510, 782, 164 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 510, 782, 164 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 510, 782, 164 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 510, 782, 164 is 2.
HCF(510, 782, 164) = 2
HCF of 510, 782, 164 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 510, 782, 164 is 2.
Highest Common Factor of 510,782,164 is 2
Step 1: Since 782 > 510, we apply the division lemma to 782 and 510, to get
782 = 510 x 1 + 272
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 272 and 510, to get
510 = 272 x 1 + 238
Step 3: We consider the new divisor 272 and the new remainder 238, and apply the division lemma to get
272 = 238 x 1 + 34
We consider the new divisor 238 and the new remainder 34, and apply the division lemma to get
238 = 34 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 510 and 782 is 34
Notice that 34 = HCF(238,34) = HCF(272,238) = HCF(510,272) = HCF(782,510) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 164 > 34, we apply the division lemma to 164 and 34, to get
164 = 34 x 4 + 28
Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 28 and 34, to get
34 = 28 x 1 + 6
Step 3: We consider the new divisor 28 and the new remainder 6, and apply the division lemma to get
28 = 6 x 4 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 34 and 164 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(34,28) = HCF(164,34) .
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Frequently Asked Questions on HCF of 510, 782, 164 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 510, 782, 164?
Answer: HCF of 510, 782, 164 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 510, 782, 164 using Euclid's Algorithm?
Answer: For arbitrary numbers 510, 782, 164 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.