Highest Common Factor of 494, 356, 697 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 494, 356, 697 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 494, 356, 697 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 494, 356, 697 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 494, 356, 697 is 1.
HCF(494, 356, 697) = 1
HCF of 494, 356, 697 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 494, 356, 697 is 1.
Highest Common Factor of 494,356,697 is 1
Step 1: Since 494 > 356, we apply the division lemma to 494 and 356, to get
494 = 356 x 1 + 138
Step 2: Since the reminder 356 ≠ 0, we apply division lemma to 138 and 356, to get
356 = 138 x 2 + 80
Step 3: We consider the new divisor 138 and the new remainder 80, and apply the division lemma to get
138 = 80 x 1 + 58
We consider the new divisor 80 and the new remainder 58,and apply the division lemma to get
80 = 58 x 1 + 22
We consider the new divisor 58 and the new remainder 22,and apply the division lemma to get
58 = 22 x 2 + 14
We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 494 and 356 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(58,22) = HCF(80,58) = HCF(138,80) = HCF(356,138) = HCF(494,356) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 697 > 2, we apply the division lemma to 697 and 2, to get
697 = 2 x 348 + 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 697 is 1
Notice that 1 = HCF(2,1) = HCF(697,2) .
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Frequently Asked Questions on HCF of 494, 356, 697 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 494, 356, 697?
Answer: HCF of 494, 356, 697 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 494, 356, 697 using Euclid's Algorithm?
Answer: For arbitrary numbers 494, 356, 697 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
