Highest Common Factor of 765, 462, 840 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, 462, 840 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 765, 462, 840 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 765, 462, 840 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, 462, 840 is 3.
HCF(765, 462, 840) = 3
HCF of 765, 462, 840 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, 462, 840 is 3.
Highest Common Factor of 765,462,840 is 3
Step 1: Since 765 > 462, we apply the division lemma to 765 and 462, to get
765 = 462 x 1 + 303
Step 2: Since the reminder 462 ≠ 0, we apply division lemma to 303 and 462, to get
462 = 303 x 1 + 159
Step 3: We consider the new divisor 303 and the new remainder 159, and apply the division lemma to get
303 = 159 x 1 + 144
We consider the new divisor 159 and the new remainder 144,and apply the division lemma to get
159 = 144 x 1 + 15
We consider the new divisor 144 and the new remainder 15,and apply the division lemma to get
144 = 15 x 9 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma 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 765 and 462 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(144,15) = HCF(159,144) = HCF(303,159) = HCF(462,303) = HCF(765,462) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 840 > 3, we apply the division lemma to 840 and 3, to get
840 = 3 x 280 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 840 is 3
Notice that 3 = HCF(840,3) .
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Frequently Asked Questions on HCF of 765, 462, 840 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, 462, 840?
Answer: HCF of 765, 462, 840 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 765, 462, 840 using Euclid's Algorithm?
Answer: For arbitrary numbers 765, 462, 840 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
