Highest Common Factor of 578, 906, 976, 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 578, 906, 976, 822 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 578, 906, 976, 822 is 2 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 578, 906, 976, 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 578, 906, 976, 822 is 2.
HCF(578, 906, 976, 822) = 2
HCF of 578, 906, 976, 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 578, 906, 976, 822 is 2.
Highest Common Factor of 578,906,976,822 is 2
Step 1: Since 906 > 578, we apply the division lemma to 906 and 578, to get
906 = 578 x 1 + 328
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 328 and 578, to get
578 = 328 x 1 + 250
Step 3: We consider the new divisor 328 and the new remainder 250, and apply the division lemma to get
328 = 250 x 1 + 78
We consider the new divisor 250 and the new remainder 78,and apply the division lemma to get
250 = 78 x 3 + 16
We consider the new divisor 78 and the new remainder 16,and apply the division lemma to get
78 = 16 x 4 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 578 and 906 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(78,16) = HCF(250,78) = HCF(328,250) = HCF(578,328) = HCF(906,578) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 976 > 2, we apply the division lemma to 976 and 2, to get
976 = 2 x 488 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 976 is 2
Notice that 2 = HCF(976,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 822 > 2, we apply the division lemma to 822 and 2, to get
822 = 2 x 411 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 822 is 2
Notice that 2 = HCF(822,2) .
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Frequently Asked Questions on HCF of 578, 906, 976, 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 578, 906, 976, 822?
Answer: HCF of 578, 906, 976, 822 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 578, 906, 976, 822 using Euclid's Algorithm?
Answer: For arbitrary numbers 578, 906, 976, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
