Highest Common Factor of 693, 294, 314 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 693, 294, 314 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 693, 294, 314 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 693, 294, 314 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 693, 294, 314 is 1.
HCF(693, 294, 314) = 1
HCF of 693, 294, 314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 693, 294, 314 is 1.
Highest Common Factor of 693,294,314 is 1
Step 1: Since 693 > 294, we apply the division lemma to 693 and 294, to get
693 = 294 x 2 + 105
Step 2: Since the reminder 294 ≠ 0, we apply division lemma to 105 and 294, to get
294 = 105 x 2 + 84
Step 3: We consider the new divisor 105 and the new remainder 84, and apply the division lemma to get
105 = 84 x 1 + 21
We consider the new divisor 84 and the new remainder 21, and apply the division lemma to get
84 = 21 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 693 and 294 is 21
Notice that 21 = HCF(84,21) = HCF(105,84) = HCF(294,105) = HCF(693,294) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 314 > 21, we apply the division lemma to 314 and 21, to get
314 = 21 x 14 + 20
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 20 and 21, to get
21 = 20 x 1 + 1
Step 3: We consider the new divisor 20 and the new remainder 1, and apply the division lemma to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 21 and 314 is 1
Notice that 1 = HCF(20,1) = HCF(21,20) = HCF(314,21) .
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Frequently Asked Questions on HCF of 693, 294, 314 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 693, 294, 314?
Answer: HCF of 693, 294, 314 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 693, 294, 314 using Euclid's Algorithm?
Answer: For arbitrary numbers 693, 294, 314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.