Highest Common Factor of 857, 128, 194 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 857, 128, 194 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 857, 128, 194 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 857, 128, 194 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 857, 128, 194 is 1.
HCF(857, 128, 194) = 1
HCF of 857, 128, 194 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 857, 128, 194 is 1.
Highest Common Factor of 857,128,194 is 1
Step 1: Since 857 > 128, we apply the division lemma to 857 and 128, to get
857 = 128 x 6 + 89
Step 2: Since the reminder 128 ≠ 0, we apply division lemma to 89 and 128, to get
128 = 89 x 1 + 39
Step 3: We consider the new divisor 89 and the new remainder 39, and apply the division lemma to get
89 = 39 x 2 + 11
We consider the new divisor 39 and the new remainder 11,and apply the division lemma to get
39 = 11 x 3 + 6
We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 857 and 128 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(39,11) = HCF(89,39) = HCF(128,89) = HCF(857,128) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 194 > 1, we apply the division lemma to 194 and 1, to get
194 = 1 x 194 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 194 is 1
Notice that 1 = HCF(194,1) .
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Frequently Asked Questions on HCF of 857, 128, 194 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 857, 128, 194?
Answer: HCF of 857, 128, 194 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 857, 128, 194 using Euclid's Algorithm?
Answer: For arbitrary numbers 857, 128, 194 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
