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 6990, 9966 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 6990, 9966 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 6990, 9966 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 6990, 9966 is 6.
HCF(6990, 9966) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6990, 9966 is 6.
Step 1: Since 9966 > 6990, we apply the division lemma to 9966 and 6990, to get
9966 = 6990 x 1 + 2976
Step 2: Since the reminder 6990 ≠ 0, we apply division lemma to 2976 and 6990, to get
6990 = 2976 x 2 + 1038
Step 3: We consider the new divisor 2976 and the new remainder 1038, and apply the division lemma to get
2976 = 1038 x 2 + 900
We consider the new divisor 1038 and the new remainder 900,and apply the division lemma to get
1038 = 900 x 1 + 138
We consider the new divisor 900 and the new remainder 138,and apply the division lemma to get
900 = 138 x 6 + 72
We consider the new divisor 138 and the new remainder 72,and apply the division lemma to get
138 = 72 x 1 + 66
We consider the new divisor 72 and the new remainder 66,and apply the division lemma to get
72 = 66 x 1 + 6
We consider the new divisor 66 and the new remainder 6,and apply the division lemma to get
66 = 6 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6990 and 9966 is 6
Notice that 6 = HCF(66,6) = HCF(72,66) = HCF(138,72) = HCF(900,138) = HCF(1038,900) = HCF(2976,1038) = HCF(6990,2976) = HCF(9966,6990) .
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 6990, 9966?
Answer: HCF of 6990, 9966 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6990, 9966 using Euclid's Algorithm?
Answer: For arbitrary numbers 6990, 9966 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.