Highest Common Factor of 908, 174, 861 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 908, 174, 861 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 908, 174, 861 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 908, 174, 861 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 908, 174, 861 is 1.
HCF(908, 174, 861) = 1
HCF of 908, 174, 861 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 908, 174, 861 is 1.
Highest Common Factor of 908,174,861 is 1
Step 1: Since 908 > 174, we apply the division lemma to 908 and 174, to get
908 = 174 x 5 + 38
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 38 and 174, to get
174 = 38 x 4 + 22
Step 3: We consider the new divisor 38 and the new remainder 22, and apply the division lemma to get
38 = 22 x 1 + 16
We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get
22 = 16 x 1 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 908 and 174 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(38,22) = HCF(174,38) = HCF(908,174) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 861 > 2, we apply the division lemma to 861 and 2, to get
861 = 2 x 430 + 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 861 is 1
Notice that 1 = HCF(2,1) = HCF(861,2) .
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Frequently Asked Questions on HCF of 908, 174, 861 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 908, 174, 861?
Answer: HCF of 908, 174, 861 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 908, 174, 861 using Euclid's Algorithm?
Answer: For arbitrary numbers 908, 174, 861 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.