Highest Common Factor of 3186, 3734 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 3186, 3734 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3186, 3734 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 3186, 3734 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 3186, 3734 is 2.
HCF(3186, 3734) = 2
HCF of 3186, 3734 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3186, 3734 is 2.
Highest Common Factor of 3186,3734 is 2
Step 1: Since 3734 > 3186, we apply the division lemma to 3734 and 3186, to get
3734 = 3186 x 1 + 548
Step 2: Since the reminder 3186 ≠ 0, we apply division lemma to 548 and 3186, to get
3186 = 548 x 5 + 446
Step 3: We consider the new divisor 548 and the new remainder 446, and apply the division lemma to get
548 = 446 x 1 + 102
We consider the new divisor 446 and the new remainder 102,and apply the division lemma to get
446 = 102 x 4 + 38
We consider the new divisor 102 and the new remainder 38,and apply the division lemma to get
102 = 38 x 2 + 26
We consider the new divisor 38 and the new remainder 26,and apply the division lemma to get
38 = 26 x 1 + 12
We consider the new divisor 26 and the new remainder 12,and apply the division lemma to get
26 = 12 x 2 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3186 and 3734 is 2
Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(38,26) = HCF(102,38) = HCF(446,102) = HCF(548,446) = HCF(3186,548) = HCF(3734,3186) .
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Frequently Asked Questions on HCF of 3186, 3734 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 3186, 3734?
Answer: HCF of 3186, 3734 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3186, 3734 using Euclid's Algorithm?
Answer: For arbitrary numbers 3186, 3734 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.