Highest Common Factor of 765, 705, 466 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 765, 705, 466 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 765, 705, 466 is 1 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 765, 705, 466 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 765, 705, 466 is 1.
HCF(765, 705, 466) = 1
HCF of 765, 705, 466 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 765, 705, 466 is 1.
Highest Common Factor of 765,705,466 is 1
Step 1: Since 765 > 705, we apply the division lemma to 765 and 705, to get
765 = 705 x 1 + 60
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 60 and 705, to get
705 = 60 x 11 + 45
Step 3: We consider the new divisor 60 and the new remainder 45, and apply the division lemma to get
60 = 45 x 1 + 15
We consider the new divisor 45 and the new remainder 15, and apply the division lemma to get
45 = 15 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 765 and 705 is 15
Notice that 15 = HCF(45,15) = HCF(60,45) = HCF(705,60) = HCF(765,705) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 466 > 15, we apply the division lemma to 466 and 15, to get
466 = 15 x 31 + 1
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 1 and 15, to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 466 is 1
Notice that 1 = HCF(15,1) = HCF(466,15) .
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Frequently Asked Questions on HCF of 765, 705, 466 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 765, 705, 466?
Answer: HCF of 765, 705, 466 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 765, 705, 466 using Euclid's Algorithm?
Answer: For arbitrary numbers 765, 705, 466 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.