Highest Common Factor of 313, 493, 693 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 313, 493, 693 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 313, 493, 693 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 313, 493, 693 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 313, 493, 693 is 1.
HCF(313, 493, 693) = 1
HCF of 313, 493, 693 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 313, 493, 693 is 1.
Highest Common Factor of 313,493,693 is 1
Step 1: Since 493 > 313, we apply the division lemma to 493 and 313, to get
493 = 313 x 1 + 180
Step 2: Since the reminder 313 ≠ 0, we apply division lemma to 180 and 313, to get
313 = 180 x 1 + 133
Step 3: We consider the new divisor 180 and the new remainder 133, and apply the division lemma to get
180 = 133 x 1 + 47
We consider the new divisor 133 and the new remainder 47,and apply the division lemma to get
133 = 47 x 2 + 39
We consider the new divisor 47 and the new remainder 39,and apply the division lemma to get
47 = 39 x 1 + 8
We consider the new divisor 39 and the new remainder 8,and apply the division lemma to get
39 = 8 x 4 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 313 and 493 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(39,8) = HCF(47,39) = HCF(133,47) = HCF(180,133) = HCF(313,180) = HCF(493,313) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 693 > 1, we apply the division lemma to 693 and 1, to get
693 = 1 x 693 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 693 is 1
Notice that 1 = HCF(693,1) .
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Frequently Asked Questions on HCF of 313, 493, 693 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 313, 493, 693?
Answer: HCF of 313, 493, 693 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 313, 493, 693 using Euclid's Algorithm?
Answer: For arbitrary numbers 313, 493, 693 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.