Highest Common Factor of 829, 314, 696, 338 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 829, 314, 696, 338 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 829, 314, 696, 338 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 829, 314, 696, 338 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 829, 314, 696, 338 is 1.
HCF(829, 314, 696, 338) = 1
HCF of 829, 314, 696, 338 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 829, 314, 696, 338 is 1.
Highest Common Factor of 829,314,696,338 is 1
Step 1: Since 829 > 314, we apply the division lemma to 829 and 314, to get
829 = 314 x 2 + 201
Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 201 and 314, to get
314 = 201 x 1 + 113
Step 3: We consider the new divisor 201 and the new remainder 113, and apply the division lemma to get
201 = 113 x 1 + 88
We consider the new divisor 113 and the new remainder 88,and apply the division lemma to get
113 = 88 x 1 + 25
We consider the new divisor 88 and the new remainder 25,and apply the division lemma to get
88 = 25 x 3 + 13
We consider the new divisor 25 and the new remainder 13,and apply the division lemma to get
25 = 13 x 1 + 12
We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get
13 = 12 x 1 + 1
We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 829 and 314 is 1
Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(25,13) = HCF(88,25) = HCF(113,88) = HCF(201,113) = HCF(314,201) = HCF(829,314) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 696 > 1, we apply the division lemma to 696 and 1, to get
696 = 1 x 696 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 696 is 1
Notice that 1 = HCF(696,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 338 > 1, we apply the division lemma to 338 and 1, to get
338 = 1 x 338 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 338 is 1
Notice that 1 = HCF(338,1) .
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Frequently Asked Questions on HCF of 829, 314, 696, 338 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 829, 314, 696, 338?
Answer: HCF of 829, 314, 696, 338 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 829, 314, 696, 338 using Euclid's Algorithm?
Answer: For arbitrary numbers 829, 314, 696, 338 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
