Highest Common Factor of 578, 682, 188 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, 682, 188 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 578, 682, 188 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, 682, 188 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, 682, 188 is 2.
HCF(578, 682, 188) = 2
HCF of 578, 682, 188 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, 682, 188 is 2.
Highest Common Factor of 578,682,188 is 2
Step 1: Since 682 > 578, we apply the division lemma to 682 and 578, to get
682 = 578 x 1 + 104
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 104 and 578, to get
578 = 104 x 5 + 58
Step 3: We consider the new divisor 104 and the new remainder 58, and apply the division lemma to get
104 = 58 x 1 + 46
We consider the new divisor 58 and the new remainder 46,and apply the division lemma to get
58 = 46 x 1 + 12
We consider the new divisor 46 and the new remainder 12,and apply the division lemma to get
46 = 12 x 3 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 578 and 682 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(46,12) = HCF(58,46) = HCF(104,58) = HCF(578,104) = HCF(682,578) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 188 > 2, we apply the division lemma to 188 and 2, to get
188 = 2 x 94 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 188 is 2
Notice that 2 = HCF(188,2) .
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Frequently Asked Questions on HCF of 578, 682, 188 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, 682, 188?
Answer: HCF of 578, 682, 188 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 578, 682, 188 using Euclid's Algorithm?
Answer: For arbitrary numbers 578, 682, 188 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.