Highest Common Factor of 313, 123 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, 123 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 313, 123 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, 123 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, 123 is 1.
HCF(313, 123) = 1
HCF of 313, 123 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, 123 is 1.
Highest Common Factor of 313,123 is 1
Step 1: Since 313 > 123, we apply the division lemma to 313 and 123, to get
313 = 123 x 2 + 67
Step 2: Since the reminder 123 ≠ 0, we apply division lemma to 67 and 123, to get
123 = 67 x 1 + 56
Step 3: We consider the new divisor 67 and the new remainder 56, and apply the division lemma to get
67 = 56 x 1 + 11
We consider the new divisor 56 and the new remainder 11,and apply the division lemma to get
56 = 11 x 5 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 313 and 123 is 1
Notice that 1 = HCF(11,1) = HCF(56,11) = HCF(67,56) = HCF(123,67) = HCF(313,123) .
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Frequently Asked Questions on HCF of 313, 123 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, 123?
Answer: HCF of 313, 123 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 313, 123 using Euclid's Algorithm?
Answer: For arbitrary numbers 313, 123 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.