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 6714, 3036 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 6714, 3036 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 6714, 3036 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 6714, 3036 is 6.
HCF(6714, 3036) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6714, 3036 is 6.
Step 1: Since 6714 > 3036, we apply the division lemma to 6714 and 3036, to get
6714 = 3036 x 2 + 642
Step 2: Since the reminder 3036 ≠ 0, we apply division lemma to 642 and 3036, to get
3036 = 642 x 4 + 468
Step 3: We consider the new divisor 642 and the new remainder 468, and apply the division lemma to get
642 = 468 x 1 + 174
We consider the new divisor 468 and the new remainder 174,and apply the division lemma to get
468 = 174 x 2 + 120
We consider the new divisor 174 and the new remainder 120,and apply the division lemma to get
174 = 120 x 1 + 54
We consider the new divisor 120 and the new remainder 54,and apply the division lemma to get
120 = 54 x 2 + 12
We consider the new divisor 54 and the new remainder 12,and apply the division lemma to get
54 = 12 x 4 + 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 6714 and 3036 is 6
Notice that 6 = HCF(12,6) = HCF(54,12) = HCF(120,54) = HCF(174,120) = HCF(468,174) = HCF(642,468) = HCF(3036,642) = HCF(6714,3036) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 6714, 3036?
Answer: HCF of 6714, 3036 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6714, 3036 using Euclid's Algorithm?
Answer: For arbitrary numbers 6714, 3036 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.