Highest Common Factor of 765, 570, 822 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, 570, 822 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 765, 570, 822 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, 570, 822 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, 570, 822 is 3.
HCF(765, 570, 822) = 3
HCF of 765, 570, 822 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, 570, 822 is 3.
Highest Common Factor of 765,570,822 is 3
Step 1: Since 765 > 570, we apply the division lemma to 765 and 570, to get
765 = 570 x 1 + 195
Step 2: Since the reminder 570 ≠ 0, we apply division lemma to 195 and 570, to get
570 = 195 x 2 + 180
Step 3: We consider the new divisor 195 and the new remainder 180, and apply the division lemma to get
195 = 180 x 1 + 15
We consider the new divisor 180 and the new remainder 15, and apply the division lemma to get
180 = 15 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 765 and 570 is 15
Notice that 15 = HCF(180,15) = HCF(195,180) = HCF(570,195) = HCF(765,570) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 822 > 15, we apply the division lemma to 822 and 15, to get
822 = 15 x 54 + 12
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 12 and 15, to get
15 = 12 x 1 + 3
Step 3: We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 822 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(822,15) .
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Frequently Asked Questions on HCF of 765, 570, 822 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, 570, 822?
Answer: HCF of 765, 570, 822 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 765, 570, 822 using Euclid's Algorithm?
Answer: For arbitrary numbers 765, 570, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.