Highest Common Factor of 3331, 8223, 21747 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 3331, 8223, 21747 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3331, 8223, 21747 is 1 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 3331, 8223, 21747 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 3331, 8223, 21747 is 1.
HCF(3331, 8223, 21747) = 1
HCF of 3331, 8223, 21747 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3331, 8223, 21747 is 1.
Highest Common Factor of 3331,8223,21747 is 1
Step 1: Since 8223 > 3331, we apply the division lemma to 8223 and 3331, to get
8223 = 3331 x 2 + 1561
Step 2: Since the reminder 3331 ≠ 0, we apply division lemma to 1561 and 3331, to get
3331 = 1561 x 2 + 209
Step 3: We consider the new divisor 1561 and the new remainder 209, and apply the division lemma to get
1561 = 209 x 7 + 98
We consider the new divisor 209 and the new remainder 98,and apply the division lemma to get
209 = 98 x 2 + 13
We consider the new divisor 98 and the new remainder 13,and apply the division lemma to get
98 = 13 x 7 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3331 and 8223 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(98,13) = HCF(209,98) = HCF(1561,209) = HCF(3331,1561) = HCF(8223,3331) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21747 > 1, we apply the division lemma to 21747 and 1, to get
21747 = 1 x 21747 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21747 is 1
Notice that 1 = HCF(21747,1) .
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Frequently Asked Questions on HCF of 3331, 8223, 21747 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 3331, 8223, 21747?
Answer: HCF of 3331, 8223, 21747 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3331, 8223, 21747 using Euclid's Algorithm?
Answer: For arbitrary numbers 3331, 8223, 21747 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
