Highest Common Factor of 765, 664 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, 664 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 765, 664 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, 664 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, 664 is 1.
HCF(765, 664) = 1
HCF of 765, 664 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, 664 is 1.
Highest Common Factor of 765,664 is 1
Step 1: Since 765 > 664, we apply the division lemma to 765 and 664, to get
765 = 664 x 1 + 101
Step 2: Since the reminder 664 ≠ 0, we apply division lemma to 101 and 664, to get
664 = 101 x 6 + 58
Step 3: We consider the new divisor 101 and the new remainder 58, and apply the division lemma to get
101 = 58 x 1 + 43
We consider the new divisor 58 and the new remainder 43,and apply the division lemma to get
58 = 43 x 1 + 15
We consider the new divisor 43 and the new remainder 15,and apply the division lemma to get
43 = 15 x 2 + 13
We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get
15 = 13 x 1 + 2
We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get
13 = 2 x 6 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 765 and 664 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(43,15) = HCF(58,43) = HCF(101,58) = HCF(664,101) = HCF(765,664) .
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Frequently Asked Questions on HCF of 765, 664 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, 664?
Answer: HCF of 765, 664 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 765, 664 using Euclid's Algorithm?
Answer: For arbitrary numbers 765, 664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
