Highest Common Factor of 3340, 3978 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 3340, 3978 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3340, 3978 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 3340, 3978 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 3340, 3978 is 2.
HCF(3340, 3978) = 2
HCF of 3340, 3978 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3340, 3978 is 2.
Highest Common Factor of 3340,3978 is 2
Step 1: Since 3978 > 3340, we apply the division lemma to 3978 and 3340, to get
3978 = 3340 x 1 + 638
Step 2: Since the reminder 3340 ≠ 0, we apply division lemma to 638 and 3340, to get
3340 = 638 x 5 + 150
Step 3: We consider the new divisor 638 and the new remainder 150, and apply the division lemma to get
638 = 150 x 4 + 38
We consider the new divisor 150 and the new remainder 38,and apply the division lemma to get
150 = 38 x 3 + 36
We consider the new divisor 38 and the new remainder 36,and apply the division lemma to get
38 = 36 x 1 + 2
We consider the new divisor 36 and the new remainder 2,and apply the division lemma to get
36 = 2 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3340 and 3978 is 2
Notice that 2 = HCF(36,2) = HCF(38,36) = HCF(150,38) = HCF(638,150) = HCF(3340,638) = HCF(3978,3340) .
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Frequently Asked Questions on HCF of 3340, 3978 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 3340, 3978?
Answer: HCF of 3340, 3978 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3340, 3978 using Euclid's Algorithm?
Answer: For arbitrary numbers 3340, 3978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.