Highest Common Factor of 9036, 6722 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 9036, 6722 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9036, 6722 is 2 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 9036, 6722 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 9036, 6722 is 2.
HCF(9036, 6722) = 2
HCF of 9036, 6722 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9036, 6722 is 2.
Highest Common Factor of 9036,6722 is 2
Step 1: Since 9036 > 6722, we apply the division lemma to 9036 and 6722, to get
9036 = 6722 x 1 + 2314
Step 2: Since the reminder 6722 ≠ 0, we apply division lemma to 2314 and 6722, to get
6722 = 2314 x 2 + 2094
Step 3: We consider the new divisor 2314 and the new remainder 2094, and apply the division lemma to get
2314 = 2094 x 1 + 220
We consider the new divisor 2094 and the new remainder 220,and apply the division lemma to get
2094 = 220 x 9 + 114
We consider the new divisor 220 and the new remainder 114,and apply the division lemma to get
220 = 114 x 1 + 106
We consider the new divisor 114 and the new remainder 106,and apply the division lemma to get
114 = 106 x 1 + 8
We consider the new divisor 106 and the new remainder 8,and apply the division lemma to get
106 = 8 x 13 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9036 and 6722 is 2
Notice that 2 = HCF(8,2) = HCF(106,8) = HCF(114,106) = HCF(220,114) = HCF(2094,220) = HCF(2314,2094) = HCF(6722,2314) = HCF(9036,6722) .
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Frequently Asked Questions on HCF of 9036, 6722 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 9036, 6722?
Answer: HCF of 9036, 6722 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9036, 6722 using Euclid's Algorithm?
Answer: For arbitrary numbers 9036, 6722 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.