Highest Common Factor of 681, 564, 116, 178 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 681, 564, 116, 178 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 681, 564, 116, 178 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 681, 564, 116, 178 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 681, 564, 116, 178 is 1.
HCF(681, 564, 116, 178) = 1
HCF of 681, 564, 116, 178 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 681, 564, 116, 178 is 1.
Highest Common Factor of 681,564,116,178 is 1
Step 1: Since 681 > 564, we apply the division lemma to 681 and 564, to get
681 = 564 x 1 + 117
Step 2: Since the reminder 564 ≠ 0, we apply division lemma to 117 and 564, to get
564 = 117 x 4 + 96
Step 3: We consider the new divisor 117 and the new remainder 96, and apply the division lemma to get
117 = 96 x 1 + 21
We consider the new divisor 96 and the new remainder 21,and apply the division lemma to get
96 = 21 x 4 + 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 681 and 564 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(96,21) = HCF(117,96) = HCF(564,117) = HCF(681,564) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 116 > 3, we apply the division lemma to 116 and 3, to get
116 = 3 x 38 + 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 116 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(116,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 178 > 1, we apply the division lemma to 178 and 1, to get
178 = 1 x 178 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 178 is 1
Notice that 1 = HCF(178,1) .
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Frequently Asked Questions on HCF of 681, 564, 116, 178 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 681, 564, 116, 178?
Answer: HCF of 681, 564, 116, 178 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 681, 564, 116, 178 using Euclid's Algorithm?
Answer: For arbitrary numbers 681, 564, 116, 178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.