Highest Common Factor of 510, 1806, 2134 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, 1806, 2134 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 510, 1806, 2134 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, 1806, 2134 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, 1806, 2134 is 2.
HCF(510, 1806, 2134) = 2
HCF of 510, 1806, 2134 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, 1806, 2134 is 2.
Highest Common Factor of 510,1806,2134 is 2
Step 1: Since 1806 > 510, we apply the division lemma to 1806 and 510, to get
1806 = 510 x 3 + 276
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 276 and 510, to get
510 = 276 x 1 + 234
Step 3: We consider the new divisor 276 and the new remainder 234, and apply the division lemma to get
276 = 234 x 1 + 42
We consider the new divisor 234 and the new remainder 42,and apply the division lemma to get
234 = 42 x 5 + 24
We consider the new divisor 42 and the new remainder 24,and apply the division lemma to get
42 = 24 x 1 + 18
We consider the new divisor 24 and the new remainder 18,and apply the division lemma to get
24 = 18 x 1 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 510 and 1806 is 6
Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(42,24) = HCF(234,42) = HCF(276,234) = HCF(510,276) = HCF(1806,510) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2134 > 6, we apply the division lemma to 2134 and 6, to get
2134 = 6 x 355 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: 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 6 and 2134 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(2134,6) .
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Frequently Asked Questions on HCF of 510, 1806, 2134 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, 1806, 2134?
Answer: HCF of 510, 1806, 2134 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 510, 1806, 2134 using Euclid's Algorithm?
Answer: For arbitrary numbers 510, 1806, 2134 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.