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 822, 9579, 9668 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 822, 9579, 9668 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 822, 9579, 9668 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 822, 9579, 9668 is 1.
HCF(822, 9579, 9668) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 822, 9579, 9668 is 1.
Step 1: Since 9579 > 822, we apply the division lemma to 9579 and 822, to get
9579 = 822 x 11 + 537
Step 2: Since the reminder 822 ≠ 0, we apply division lemma to 537 and 822, to get
822 = 537 x 1 + 285
Step 3: We consider the new divisor 537 and the new remainder 285, and apply the division lemma to get
537 = 285 x 1 + 252
We consider the new divisor 285 and the new remainder 252,and apply the division lemma to get
285 = 252 x 1 + 33
We consider the new divisor 252 and the new remainder 33,and apply the division lemma to get
252 = 33 x 7 + 21
We consider the new divisor 33 and the new remainder 21,and apply the division lemma to get
33 = 21 x 1 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 822 and 9579 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(252,33) = HCF(285,252) = HCF(537,285) = HCF(822,537) = HCF(9579,822) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9668 > 3, we apply the division lemma to 9668 and 3, to get
9668 = 3 x 3222 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 9668 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(9668,3) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 822, 9579, 9668?
Answer: HCF of 822, 9579, 9668 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 822, 9579, 9668 using Euclid's Algorithm?
Answer: For arbitrary numbers 822, 9579, 9668 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.