Highest Common Factor of 578, 660, 891 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, 660, 891 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 578, 660, 891 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 578, 660, 891 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, 660, 891 is 1.
HCF(578, 660, 891) = 1
HCF of 578, 660, 891 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, 660, 891 is 1.
Highest Common Factor of 578,660,891 is 1
Step 1: Since 660 > 578, we apply the division lemma to 660 and 578, to get
660 = 578 x 1 + 82
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 82 and 578, to get
578 = 82 x 7 + 4
Step 3: We consider the new divisor 82 and the new remainder 4, and apply the division lemma to get
82 = 4 x 20 + 2
We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 578 and 660 is 2
Notice that 2 = HCF(4,2) = HCF(82,4) = HCF(578,82) = HCF(660,578) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 891 > 2, we apply the division lemma to 891 and 2, to get
891 = 2 x 445 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 891 is 1
Notice that 1 = HCF(2,1) = HCF(891,2) .
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Frequently Asked Questions on HCF of 578, 660, 891 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, 660, 891?
Answer: HCF of 578, 660, 891 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 578, 660, 891 using Euclid's Algorithm?
Answer: For arbitrary numbers 578, 660, 891 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.