Highest Common Factor of 762, 464, 710 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 762, 464, 710 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 762, 464, 710 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 762, 464, 710 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 762, 464, 710 is 2.
HCF(762, 464, 710) = 2
HCF of 762, 464, 710 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 762, 464, 710 is 2.
Highest Common Factor of 762,464,710 is 2
Step 1: Since 762 > 464, we apply the division lemma to 762 and 464, to get
762 = 464 x 1 + 298
Step 2: Since the reminder 464 ≠ 0, we apply division lemma to 298 and 464, to get
464 = 298 x 1 + 166
Step 3: We consider the new divisor 298 and the new remainder 166, and apply the division lemma to get
298 = 166 x 1 + 132
We consider the new divisor 166 and the new remainder 132,and apply the division lemma to get
166 = 132 x 1 + 34
We consider the new divisor 132 and the new remainder 34,and apply the division lemma to get
132 = 34 x 3 + 30
We consider the new divisor 34 and the new remainder 30,and apply the division lemma to get
34 = 30 x 1 + 4
We consider the new divisor 30 and the new remainder 4,and apply the division lemma to get
30 = 4 x 7 + 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 762 and 464 is 2
Notice that 2 = HCF(4,2) = HCF(30,4) = HCF(34,30) = HCF(132,34) = HCF(166,132) = HCF(298,166) = HCF(464,298) = HCF(762,464) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 710 > 2, we apply the division lemma to 710 and 2, to get
710 = 2 x 355 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 710 is 2
Notice that 2 = HCF(710,2) .
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Frequently Asked Questions on HCF of 762, 464, 710 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 762, 464, 710?
Answer: HCF of 762, 464, 710 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 762, 464, 710 using Euclid's Algorithm?
Answer: For arbitrary numbers 762, 464, 710 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.