Highest Common Factor of 3970, 3678 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 3970, 3678 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3970, 3678 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 3970, 3678 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 3970, 3678 is 2.
HCF(3970, 3678) = 2
HCF of 3970, 3678 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3970, 3678 is 2.
Highest Common Factor of 3970,3678 is 2
Step 1: Since 3970 > 3678, we apply the division lemma to 3970 and 3678, to get
3970 = 3678 x 1 + 292
Step 2: Since the reminder 3678 ≠ 0, we apply division lemma to 292 and 3678, to get
3678 = 292 x 12 + 174
Step 3: We consider the new divisor 292 and the new remainder 174, and apply the division lemma to get
292 = 174 x 1 + 118
We consider the new divisor 174 and the new remainder 118,and apply the division lemma to get
174 = 118 x 1 + 56
We consider the new divisor 118 and the new remainder 56,and apply the division lemma to get
118 = 56 x 2 + 6
We consider the new divisor 56 and the new remainder 6,and apply the division lemma to get
56 = 6 x 9 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3970 and 3678 is 2
Notice that 2 = HCF(6,2) = HCF(56,6) = HCF(118,56) = HCF(174,118) = HCF(292,174) = HCF(3678,292) = HCF(3970,3678) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 3970, 3678 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 3970, 3678?
Answer: HCF of 3970, 3678 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3970, 3678 using Euclid's Algorithm?
Answer: For arbitrary numbers 3970, 3678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.