Highest Common Factor of 765, 998, 82 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, 998, 82 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 765, 998, 82 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, 998, 82 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, 998, 82 is 1.
HCF(765, 998, 82) = 1
HCF of 765, 998, 82 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, 998, 82 is 1.
Highest Common Factor of 765,998,82 is 1
Step 1: Since 998 > 765, we apply the division lemma to 998 and 765, to get
998 = 765 x 1 + 233
Step 2: Since the reminder 765 ≠ 0, we apply division lemma to 233 and 765, to get
765 = 233 x 3 + 66
Step 3: We consider the new divisor 233 and the new remainder 66, and apply the division lemma to get
233 = 66 x 3 + 35
We consider the new divisor 66 and the new remainder 35,and apply the division lemma to get
66 = 35 x 1 + 31
We consider the new divisor 35 and the new remainder 31,and apply the division lemma to get
35 = 31 x 1 + 4
We consider the new divisor 31 and the new remainder 4,and apply the division lemma to get
31 = 4 x 7 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 765 and 998 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(31,4) = HCF(35,31) = HCF(66,35) = HCF(233,66) = HCF(765,233) = HCF(998,765) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 82 > 1, we apply the division lemma to 82 and 1, to get
82 = 1 x 82 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 82 is 1
Notice that 1 = HCF(82,1) .
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Frequently Asked Questions on HCF of 765, 998, 82 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, 998, 82?
Answer: HCF of 765, 998, 82 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 765, 998, 82 using Euclid's Algorithm?
Answer: For arbitrary numbers 765, 998, 82 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.