Highest Common Factor of 768, 210, 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 768, 210, 765 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 768, 210, 765 is 3 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 768, 210, 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 768, 210, 765 is 3.
HCF(768, 210, 765) = 3
HCF of 768, 210, 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 768, 210, 765 is 3.
Highest Common Factor of 768,210,765 is 3
Step 1: Since 768 > 210, we apply the division lemma to 768 and 210, to get
768 = 210 x 3 + 138
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 138 and 210, to get
210 = 138 x 1 + 72
Step 3: We consider the new divisor 138 and the new remainder 72, and apply the division lemma to get
138 = 72 x 1 + 66
We consider the new divisor 72 and the new remainder 66,and apply the division lemma to get
72 = 66 x 1 + 6
We consider the new divisor 66 and the new remainder 6,and apply the division lemma to get
66 = 6 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 768 and 210 is 6
Notice that 6 = HCF(66,6) = HCF(72,66) = HCF(138,72) = HCF(210,138) = HCF(768,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 765 > 6, we apply the division lemma to 765 and 6, to get
765 = 6 x 127 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 765 is 3
Notice that 3 = HCF(6,3) = HCF(765,6) .
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Frequently Asked Questions on HCF of 768, 210, 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 768, 210, 765?
Answer: HCF of 768, 210, 765 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 768, 210, 765 using Euclid's Algorithm?
Answer: For arbitrary numbers 768, 210, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.