Highest Common Factor of 510, 830, 114 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, 830, 114 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 510, 830, 114 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, 830, 114 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, 830, 114 is 2.
HCF(510, 830, 114) = 2
HCF of 510, 830, 114 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, 830, 114 is 2.
Highest Common Factor of 510,830,114 is 2
Step 1: Since 830 > 510, we apply the division lemma to 830 and 510, to get
830 = 510 x 1 + 320
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 320 and 510, to get
510 = 320 x 1 + 190
Step 3: We consider the new divisor 320 and the new remainder 190, and apply the division lemma to get
320 = 190 x 1 + 130
We consider the new divisor 190 and the new remainder 130,and apply the division lemma to get
190 = 130 x 1 + 60
We consider the new divisor 130 and the new remainder 60,and apply the division lemma to get
130 = 60 x 2 + 10
We consider the new divisor 60 and the new remainder 10,and apply the division lemma to get
60 = 10 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 510 and 830 is 10
Notice that 10 = HCF(60,10) = HCF(130,60) = HCF(190,130) = HCF(320,190) = HCF(510,320) = HCF(830,510) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 114 > 10, we apply the division lemma to 114 and 10, to get
114 = 10 x 11 + 4
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 4 and 10, to get
10 = 4 x 2 + 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 10 and 114 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(114,10) .
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Frequently Asked Questions on HCF of 510, 830, 114 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, 830, 114?
Answer: HCF of 510, 830, 114 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 510, 830, 114 using Euclid's Algorithm?
Answer: For arbitrary numbers 510, 830, 114 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
