Highest Common Factor of 872, 313 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 872, 313 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 872, 313 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 872, 313 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 872, 313 is 1.
HCF(872, 313) = 1
HCF of 872, 313 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 872, 313 is 1.
Highest Common Factor of 872,313 is 1
Step 1: Since 872 > 313, we apply the division lemma to 872 and 313, to get
872 = 313 x 2 + 246
Step 2: Since the reminder 313 ≠ 0, we apply division lemma to 246 and 313, to get
313 = 246 x 1 + 67
Step 3: We consider the new divisor 246 and the new remainder 67, and apply the division lemma to get
246 = 67 x 3 + 45
We consider the new divisor 67 and the new remainder 45,and apply the division lemma to get
67 = 45 x 1 + 22
We consider the new divisor 45 and the new remainder 22,and apply the division lemma to get
45 = 22 x 2 + 1
We consider the new divisor 22 and the new remainder 1,and apply the division lemma to get
22 = 1 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 872 and 313 is 1
Notice that 1 = HCF(22,1) = HCF(45,22) = HCF(67,45) = HCF(246,67) = HCF(313,246) = HCF(872,313) .
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Frequently Asked Questions on HCF of 872, 313 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 872, 313?
Answer: HCF of 872, 313 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 872, 313 using Euclid's Algorithm?
Answer: For arbitrary numbers 872, 313 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.