Highest Common Factor of 683, 874, 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 683, 874, 178 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 683, 874, 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 683, 874, 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 683, 874, 178 is 1.
HCF(683, 874, 178) = 1
HCF of 683, 874, 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 683, 874, 178 is 1.
Highest Common Factor of 683,874,178 is 1
Step 1: Since 874 > 683, we apply the division lemma to 874 and 683, to get
874 = 683 x 1 + 191
Step 2: Since the reminder 683 ≠ 0, we apply division lemma to 191 and 683, to get
683 = 191 x 3 + 110
Step 3: We consider the new divisor 191 and the new remainder 110, and apply the division lemma to get
191 = 110 x 1 + 81
We consider the new divisor 110 and the new remainder 81,and apply the division lemma to get
110 = 81 x 1 + 29
We consider the new divisor 81 and the new remainder 29,and apply the division lemma to get
81 = 29 x 2 + 23
We consider the new divisor 29 and the new remainder 23,and apply the division lemma to get
29 = 23 x 1 + 6
We consider the new divisor 23 and the new remainder 6,and apply the division lemma to get
23 = 6 x 3 + 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 683 and 874 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(23,6) = HCF(29,23) = HCF(81,29) = HCF(110,81) = HCF(191,110) = HCF(683,191) = HCF(874,683) .
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 683, 874, 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 683, 874, 178?
Answer: HCF of 683, 874, 178 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 683, 874, 178 using Euclid's Algorithm?
Answer: For arbitrary numbers 683, 874, 178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.