Highest Common Factor of 912, 10618 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 912, 10618 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 912, 10618 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 912, 10618 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 912, 10618 is 2.
HCF(912, 10618) = 2
HCF of 912, 10618 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 912, 10618 is 2.
Highest Common Factor of 912,10618 is 2
Step 1: Since 10618 > 912, we apply the division lemma to 10618 and 912, to get
10618 = 912 x 11 + 586
Step 2: Since the reminder 912 ≠ 0, we apply division lemma to 586 and 912, to get
912 = 586 x 1 + 326
Step 3: We consider the new divisor 586 and the new remainder 326, and apply the division lemma to get
586 = 326 x 1 + 260
We consider the new divisor 326 and the new remainder 260,and apply the division lemma to get
326 = 260 x 1 + 66
We consider the new divisor 260 and the new remainder 66,and apply the division lemma to get
260 = 66 x 3 + 62
We consider the new divisor 66 and the new remainder 62,and apply the division lemma to get
66 = 62 x 1 + 4
We consider the new divisor 62 and the new remainder 4,and apply the division lemma to get
62 = 4 x 15 + 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 912 and 10618 is 2
Notice that 2 = HCF(4,2) = HCF(62,4) = HCF(66,62) = HCF(260,66) = HCF(326,260) = HCF(586,326) = HCF(912,586) = HCF(10618,912) .
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Frequently Asked Questions on HCF of 912, 10618 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 912, 10618?
Answer: HCF of 912, 10618 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 912, 10618 using Euclid's Algorithm?
Answer: For arbitrary numbers 912, 10618 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.