Highest Common Factor of 7836, 6666 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 7836, 6666 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 7836, 6666 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 7836, 6666 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 7836, 6666 is 6.
HCF(7836, 6666) = 6
HCF of 7836, 6666 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7836, 6666 is 6.
Highest Common Factor of 7836,6666 is 6
Step 1: Since 7836 > 6666, we apply the division lemma to 7836 and 6666, to get
7836 = 6666 x 1 + 1170
Step 2: Since the reminder 6666 ≠ 0, we apply division lemma to 1170 and 6666, to get
6666 = 1170 x 5 + 816
Step 3: We consider the new divisor 1170 and the new remainder 816, and apply the division lemma to get
1170 = 816 x 1 + 354
We consider the new divisor 816 and the new remainder 354,and apply the division lemma to get
816 = 354 x 2 + 108
We consider the new divisor 354 and the new remainder 108,and apply the division lemma to get
354 = 108 x 3 + 30
We consider the new divisor 108 and the new remainder 30,and apply the division lemma to get
108 = 30 x 3 + 18
We consider the new divisor 30 and the new remainder 18,and apply the division lemma to get
30 = 18 x 1 + 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 7836 and 6666 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(108,30) = HCF(354,108) = HCF(816,354) = HCF(1170,816) = HCF(6666,1170) = HCF(7836,6666) .
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Frequently Asked Questions on HCF of 7836, 6666 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 7836, 6666?
Answer: HCF of 7836, 6666 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7836, 6666 using Euclid's Algorithm?
Answer: For arbitrary numbers 7836, 6666 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.