Highest Common Factor of 9102, 6990 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 9102, 6990 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 9102, 6990 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 9102, 6990 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 9102, 6990 is 6.
HCF(9102, 6990) = 6
HCF of 9102, 6990 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9102, 6990 is 6.
Highest Common Factor of 9102,6990 is 6
Step 1: Since 9102 > 6990, we apply the division lemma to 9102 and 6990, to get
9102 = 6990 x 1 + 2112
Step 2: Since the reminder 6990 ≠ 0, we apply division lemma to 2112 and 6990, to get
6990 = 2112 x 3 + 654
Step 3: We consider the new divisor 2112 and the new remainder 654, and apply the division lemma to get
2112 = 654 x 3 + 150
We consider the new divisor 654 and the new remainder 150,and apply the division lemma to get
654 = 150 x 4 + 54
We consider the new divisor 150 and the new remainder 54,and apply the division lemma to get
150 = 54 x 2 + 42
We consider the new divisor 54 and the new remainder 42,and apply the division lemma to get
54 = 42 x 1 + 12
We consider the new divisor 42 and the new remainder 12,and apply the division lemma to get
42 = 12 x 3 + 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 9102 and 6990 is 6
Notice that 6 = HCF(12,6) = HCF(42,12) = HCF(54,42) = HCF(150,54) = HCF(654,150) = HCF(2112,654) = HCF(6990,2112) = HCF(9102,6990) .
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Frequently Asked Questions on HCF of 9102, 6990 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 9102, 6990?
Answer: HCF of 9102, 6990 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9102, 6990 using Euclid's Algorithm?
Answer: For arbitrary numbers 9102, 6990 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.