Highest Common Factor of 188, 912, 614, 841 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 188, 912, 614, 841 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 188, 912, 614, 841 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 188, 912, 614, 841 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 188, 912, 614, 841 is 1.
HCF(188, 912, 614, 841) = 1
HCF of 188, 912, 614, 841 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 188, 912, 614, 841 is 1.
Highest Common Factor of 188,912,614,841 is 1
Step 1: Since 912 > 188, we apply the division lemma to 912 and 188, to get
912 = 188 x 4 + 160
Step 2: Since the reminder 188 ≠ 0, we apply division lemma to 160 and 188, to get
188 = 160 x 1 + 28
Step 3: We consider the new divisor 160 and the new remainder 28, and apply the division lemma to get
160 = 28 x 5 + 20
We consider the new divisor 28 and the new remainder 20,and apply the division lemma to get
28 = 20 x 1 + 8
We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get
20 = 8 x 2 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 188 and 912 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(28,20) = HCF(160,28) = HCF(188,160) = HCF(912,188) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 614 > 4, we apply the division lemma to 614 and 4, to get
614 = 4 x 153 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 614 is 2
Notice that 2 = HCF(4,2) = HCF(614,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 841 > 2, we apply the division lemma to 841 and 2, to get
841 = 2 x 420 + 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 841 is 1
Notice that 1 = HCF(2,1) = HCF(841,2) .
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Frequently Asked Questions on HCF of 188, 912, 614, 841 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 188, 912, 614, 841?
Answer: HCF of 188, 912, 614, 841 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 188, 912, 614, 841 using Euclid's Algorithm?
Answer: For arbitrary numbers 188, 912, 614, 841 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.