Highest Common Factor of 3714, 1044 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 3714, 1044 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 3714, 1044 is 6 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 3714, 1044 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 3714, 1044 is 6.
HCF(3714, 1044) = 6
HCF of 3714, 1044 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3714, 1044 is 6.
Highest Common Factor of 3714,1044 is 6
Step 1: Since 3714 > 1044, we apply the division lemma to 3714 and 1044, to get
3714 = 1044 x 3 + 582
Step 2: Since the reminder 1044 ≠ 0, we apply division lemma to 582 and 1044, to get
1044 = 582 x 1 + 462
Step 3: We consider the new divisor 582 and the new remainder 462, and apply the division lemma to get
582 = 462 x 1 + 120
We consider the new divisor 462 and the new remainder 120,and apply the division lemma to get
462 = 120 x 3 + 102
We consider the new divisor 120 and the new remainder 102,and apply the division lemma to get
120 = 102 x 1 + 18
We consider the new divisor 102 and the new remainder 18,and apply the division lemma to get
102 = 18 x 5 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 3714 and 1044 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(102,18) = HCF(120,102) = HCF(462,120) = HCF(582,462) = HCF(1044,582) = HCF(3714,1044) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 3714, 1044 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 3714, 1044?
Answer: HCF of 3714, 1044 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3714, 1044 using Euclid's Algorithm?
Answer: For arbitrary numbers 3714, 1044 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.