Highest Common Factor of 1965, 3714 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 1965, 3714 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1965, 3714 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 1965, 3714 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 1965, 3714 is 3.
HCF(1965, 3714) = 3
HCF of 1965, 3714 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1965, 3714 is 3.
Highest Common Factor of 1965,3714 is 3
Step 1: Since 3714 > 1965, we apply the division lemma to 3714 and 1965, to get
3714 = 1965 x 1 + 1749
Step 2: Since the reminder 1965 ≠ 0, we apply division lemma to 1749 and 1965, to get
1965 = 1749 x 1 + 216
Step 3: We consider the new divisor 1749 and the new remainder 216, and apply the division lemma to get
1749 = 216 x 8 + 21
We consider the new divisor 216 and the new remainder 21,and apply the division lemma to get
216 = 21 x 10 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1965 and 3714 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(216,21) = HCF(1749,216) = HCF(1965,1749) = HCF(3714,1965) .
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Frequently Asked Questions on HCF of 1965, 3714 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 1965, 3714?
Answer: HCF of 1965, 3714 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1965, 3714 using Euclid's Algorithm?
Answer: For arbitrary numbers 1965, 3714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.