Highest Common Factor of 9804, 8310, 32236 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 9804, 8310, 32236 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9804, 8310, 32236 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 9804, 8310, 32236 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 9804, 8310, 32236 is 2.
HCF(9804, 8310, 32236) = 2
HCF of 9804, 8310, 32236 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9804, 8310, 32236 is 2.
Highest Common Factor of 9804,8310,32236 is 2
Step 1: Since 9804 > 8310, we apply the division lemma to 9804 and 8310, to get
9804 = 8310 x 1 + 1494
Step 2: Since the reminder 8310 ≠ 0, we apply division lemma to 1494 and 8310, to get
8310 = 1494 x 5 + 840
Step 3: We consider the new divisor 1494 and the new remainder 840, and apply the division lemma to get
1494 = 840 x 1 + 654
We consider the new divisor 840 and the new remainder 654,and apply the division lemma to get
840 = 654 x 1 + 186
We consider the new divisor 654 and the new remainder 186,and apply the division lemma to get
654 = 186 x 3 + 96
We consider the new divisor 186 and the new remainder 96,and apply the division lemma to get
186 = 96 x 1 + 90
We consider the new divisor 96 and the new remainder 90,and apply the division lemma to get
96 = 90 x 1 + 6
We consider the new divisor 90 and the new remainder 6,and apply the division lemma to get
90 = 6 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 9804 and 8310 is 6
Notice that 6 = HCF(90,6) = HCF(96,90) = HCF(186,96) = HCF(654,186) = HCF(840,654) = HCF(1494,840) = HCF(8310,1494) = HCF(9804,8310) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32236 > 6, we apply the division lemma to 32236 and 6, to get
32236 = 6 x 5372 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 32236 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(32236,6) .
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Frequently Asked Questions on HCF of 9804, 8310, 32236 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 9804, 8310, 32236?
Answer: HCF of 9804, 8310, 32236 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9804, 8310, 32236 using Euclid's Algorithm?
Answer: For arbitrary numbers 9804, 8310, 32236 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
