Highest Common Factor of 428, 765 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 428, 765 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 428, 765 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 428, 765 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 428, 765 is 1.
HCF(428, 765) = 1
HCF of 428, 765 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 428, 765 is 1.
Highest Common Factor of 428,765 is 1
Step 1: Since 765 > 428, we apply the division lemma to 765 and 428, to get
765 = 428 x 1 + 337
Step 2: Since the reminder 428 ≠ 0, we apply division lemma to 337 and 428, to get
428 = 337 x 1 + 91
Step 3: We consider the new divisor 337 and the new remainder 91, and apply the division lemma to get
337 = 91 x 3 + 64
We consider the new divisor 91 and the new remainder 64,and apply the division lemma to get
91 = 64 x 1 + 27
We consider the new divisor 64 and the new remainder 27,and apply the division lemma to get
64 = 27 x 2 + 10
We consider the new divisor 27 and the new remainder 10,and apply the division lemma to get
27 = 10 x 2 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 428 and 765 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(27,10) = HCF(64,27) = HCF(91,64) = HCF(337,91) = HCF(428,337) = HCF(765,428) .
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Frequently Asked Questions on HCF of 428, 765 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 428, 765?
Answer: HCF of 428, 765 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 428, 765 using Euclid's Algorithm?
Answer: For arbitrary numbers 428, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
