Highest Common Factor of 765, 434, 77 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, 434, 77 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 765, 434, 77 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, 434, 77 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, 434, 77 is 1.
HCF(765, 434, 77) = 1
HCF of 765, 434, 77 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, 434, 77 is 1.
Highest Common Factor of 765,434,77 is 1
Step 1: Since 765 > 434, we apply the division lemma to 765 and 434, to get
765 = 434 x 1 + 331
Step 2: Since the reminder 434 ≠ 0, we apply division lemma to 331 and 434, to get
434 = 331 x 1 + 103
Step 3: We consider the new divisor 331 and the new remainder 103, and apply the division lemma to get
331 = 103 x 3 + 22
We consider the new divisor 103 and the new remainder 22,and apply the division lemma to get
103 = 22 x 4 + 15
We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get
22 = 15 x 1 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 765 and 434 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(103,22) = HCF(331,103) = HCF(434,331) = HCF(765,434) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 77 > 1, we apply the division lemma to 77 and 1, to get
77 = 1 x 77 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 77 is 1
Notice that 1 = HCF(77,1) .
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Frequently Asked Questions on HCF of 765, 434, 77 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, 434, 77?
Answer: HCF of 765, 434, 77 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 765, 434, 77 using Euclid's Algorithm?
Answer: For arbitrary numbers 765, 434, 77 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.