Highest Common Factor of 7614, 2010 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 7614, 2010 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 7614, 2010 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 7614, 2010 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 7614, 2010 is 6.
HCF(7614, 2010) = 6
HCF of 7614, 2010 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7614, 2010 is 6.
Highest Common Factor of 7614,2010 is 6
Step 1: Since 7614 > 2010, we apply the division lemma to 7614 and 2010, to get
7614 = 2010 x 3 + 1584
Step 2: Since the reminder 2010 ≠ 0, we apply division lemma to 1584 and 2010, to get
2010 = 1584 x 1 + 426
Step 3: We consider the new divisor 1584 and the new remainder 426, and apply the division lemma to get
1584 = 426 x 3 + 306
We consider the new divisor 426 and the new remainder 306,and apply the division lemma to get
426 = 306 x 1 + 120
We consider the new divisor 306 and the new remainder 120,and apply the division lemma to get
306 = 120 x 2 + 66
We consider the new divisor 120 and the new remainder 66,and apply the division lemma to get
120 = 66 x 1 + 54
We consider the new divisor 66 and the new remainder 54,and apply the division lemma to get
66 = 54 x 1 + 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 7614 and 2010 is 6
Notice that 6 = HCF(12,6) = HCF(54,12) = HCF(66,54) = HCF(120,66) = HCF(306,120) = HCF(426,306) = HCF(1584,426) = HCF(2010,1584) = HCF(7614,2010) .
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Frequently Asked Questions on HCF of 7614, 2010 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 7614, 2010?
Answer: HCF of 7614, 2010 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7614, 2010 using Euclid's Algorithm?
Answer: For arbitrary numbers 7614, 2010 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.