Highest Common Factor of 3213, 8694, 14253 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 3213, 8694, 14253 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 3213, 8694, 14253 is 3 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 3213, 8694, 14253 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 3213, 8694, 14253 is 3.
HCF(3213, 8694, 14253) = 3
HCF of 3213, 8694, 14253 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3213, 8694, 14253 is 3.
Highest Common Factor of 3213,8694,14253 is 3
Step 1: Since 8694 > 3213, we apply the division lemma to 8694 and 3213, to get
8694 = 3213 x 2 + 2268
Step 2: Since the reminder 3213 ≠ 0, we apply division lemma to 2268 and 3213, to get
3213 = 2268 x 1 + 945
Step 3: We consider the new divisor 2268 and the new remainder 945, and apply the division lemma to get
2268 = 945 x 2 + 378
We consider the new divisor 945 and the new remainder 378,and apply the division lemma to get
945 = 378 x 2 + 189
We consider the new divisor 378 and the new remainder 189,and apply the division lemma to get
378 = 189 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 189, the HCF of 3213 and 8694 is 189
Notice that 189 = HCF(378,189) = HCF(945,378) = HCF(2268,945) = HCF(3213,2268) = HCF(8694,3213) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 14253 > 189, we apply the division lemma to 14253 and 189, to get
14253 = 189 x 75 + 78
Step 2: Since the reminder 189 ≠ 0, we apply division lemma to 78 and 189, to get
189 = 78 x 2 + 33
Step 3: We consider the new divisor 78 and the new remainder 33, and apply the division lemma to get
78 = 33 x 2 + 12
We consider the new divisor 33 and the new remainder 12,and apply the division lemma to get
33 = 12 x 2 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 189 and 14253 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(33,12) = HCF(78,33) = HCF(189,78) = HCF(14253,189) .
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Frequently Asked Questions on HCF of 3213, 8694, 14253 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 3213, 8694, 14253?
Answer: HCF of 3213, 8694, 14253 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3213, 8694, 14253 using Euclid's Algorithm?
Answer: For arbitrary numbers 3213, 8694, 14253 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.