Highest Common Factor of 3687, 9774 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 3687, 9774 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 3687, 9774 is 3 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 3687, 9774 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 3687, 9774 is 3.
HCF(3687, 9774) = 3
HCF of 3687, 9774 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3687, 9774 is 3.
Highest Common Factor of 3687,9774 is 3
Step 1: Since 9774 > 3687, we apply the division lemma to 9774 and 3687, to get
9774 = 3687 x 2 + 2400
Step 2: Since the reminder 3687 ≠ 0, we apply division lemma to 2400 and 3687, to get
3687 = 2400 x 1 + 1287
Step 3: We consider the new divisor 2400 and the new remainder 1287, and apply the division lemma to get
2400 = 1287 x 1 + 1113
We consider the new divisor 1287 and the new remainder 1113,and apply the division lemma to get
1287 = 1113 x 1 + 174
We consider the new divisor 1113 and the new remainder 174,and apply the division lemma to get
1113 = 174 x 6 + 69
We consider the new divisor 174 and the new remainder 69,and apply the division lemma to get
174 = 69 x 2 + 36
We consider the new divisor 69 and the new remainder 36,and apply the division lemma to get
69 = 36 x 1 + 33
We consider the new divisor 36 and the new remainder 33,and apply the division lemma to get
36 = 33 x 1 + 3
We consider the new divisor 33 and the new remainder 3,and apply the division lemma to get
33 = 3 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3687 and 9774 is 3
Notice that 3 = HCF(33,3) = HCF(36,33) = HCF(69,36) = HCF(174,69) = HCF(1113,174) = HCF(1287,1113) = HCF(2400,1287) = HCF(3687,2400) = HCF(9774,3687) .
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Frequently Asked Questions on HCF of 3687, 9774 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 3687, 9774?
Answer: HCF of 3687, 9774 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3687, 9774 using Euclid's Algorithm?
Answer: For arbitrary numbers 3687, 9774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.