Highest Common Factor of 506, 11314 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 506, 11314 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 506, 11314 is 2 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 506, 11314 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 506, 11314 is 2.
HCF(506, 11314) = 2
HCF of 506, 11314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 506, 11314 is 2.
Highest Common Factor of 506,11314 is 2
Step 1: Since 11314 > 506, we apply the division lemma to 11314 and 506, to get
11314 = 506 x 22 + 182
Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 182 and 506, to get
506 = 182 x 2 + 142
Step 3: We consider the new divisor 182 and the new remainder 142, and apply the division lemma to get
182 = 142 x 1 + 40
We consider the new divisor 142 and the new remainder 40,and apply the division lemma to get
142 = 40 x 3 + 22
We consider the new divisor 40 and the new remainder 22,and apply the division lemma to get
40 = 22 x 1 + 18
We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get
22 = 18 x 1 + 4
We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get
18 = 4 x 4 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 506 and 11314 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(40,22) = HCF(142,40) = HCF(182,142) = HCF(506,182) = HCF(11314,506) .
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Frequently Asked Questions on HCF of 506, 11314 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 506, 11314?
Answer: HCF of 506, 11314 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 506, 11314 using Euclid's Algorithm?
Answer: For arbitrary numbers 506, 11314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
