Highest Common Factor of 762, 460 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, 460 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 762, 460 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, 460 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, 460 is 2.
HCF(762, 460) = 2
HCF of 762, 460 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, 460 is 2.
Highest Common Factor of 762,460 is 2
Step 1: Since 762 > 460, we apply the division lemma to 762 and 460, to get
762 = 460 x 1 + 302
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 302 and 460, to get
460 = 302 x 1 + 158
Step 3: We consider the new divisor 302 and the new remainder 158, and apply the division lemma to get
302 = 158 x 1 + 144
We consider the new divisor 158 and the new remainder 144,and apply the division lemma to get
158 = 144 x 1 + 14
We consider the new divisor 144 and the new remainder 14,and apply the division lemma to get
144 = 14 x 10 + 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 762 and 460 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(144,14) = HCF(158,144) = HCF(302,158) = HCF(460,302) = HCF(762,460) .
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Frequently Asked Questions on HCF of 762, 460 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, 460?
Answer: HCF of 762, 460 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 762, 460 using Euclid's Algorithm?
Answer: For arbitrary numbers 762, 460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.