Highest Common Factor of 765, 338 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, 338 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 765, 338 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, 338 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, 338 is 1.
HCF(765, 338) = 1
HCF of 765, 338 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, 338 is 1.
Highest Common Factor of 765,338 is 1
Step 1: Since 765 > 338, we apply the division lemma to 765 and 338, to get
765 = 338 x 2 + 89
Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 89 and 338, to get
338 = 89 x 3 + 71
Step 3: We consider the new divisor 89 and the new remainder 71, and apply the division lemma to get
89 = 71 x 1 + 18
We consider the new divisor 71 and the new remainder 18,and apply the division lemma to get
71 = 18 x 3 + 17
We consider the new divisor 18 and the new remainder 17,and apply the division lemma to get
18 = 17 x 1 + 1
We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 765 and 338 is 1
Notice that 1 = HCF(17,1) = HCF(18,17) = HCF(71,18) = HCF(89,71) = HCF(338,89) = HCF(765,338) .
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Frequently Asked Questions on HCF of 765, 338 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, 338?
Answer: HCF of 765, 338 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 765, 338 using Euclid's Algorithm?
Answer: For arbitrary numbers 765, 338 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.