Highest Common Factor of 8456, 3234 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 8456, 3234 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 8456, 3234 is 14 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 8456, 3234 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 8456, 3234 is 14.
HCF(8456, 3234) = 14
HCF of 8456, 3234 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8456, 3234 is 14.
Highest Common Factor of 8456,3234 is 14
Step 1: Since 8456 > 3234, we apply the division lemma to 8456 and 3234, to get
8456 = 3234 x 2 + 1988
Step 2: Since the reminder 3234 ≠ 0, we apply division lemma to 1988 and 3234, to get
3234 = 1988 x 1 + 1246
Step 3: We consider the new divisor 1988 and the new remainder 1246, and apply the division lemma to get
1988 = 1246 x 1 + 742
We consider the new divisor 1246 and the new remainder 742,and apply the division lemma to get
1246 = 742 x 1 + 504
We consider the new divisor 742 and the new remainder 504,and apply the division lemma to get
742 = 504 x 1 + 238
We consider the new divisor 504 and the new remainder 238,and apply the division lemma to get
504 = 238 x 2 + 28
We consider the new divisor 238 and the new remainder 28,and apply the division lemma to get
238 = 28 x 8 + 14
We consider the new divisor 28 and the new remainder 14,and apply the division lemma to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 8456 and 3234 is 14
Notice that 14 = HCF(28,14) = HCF(238,28) = HCF(504,238) = HCF(742,504) = HCF(1246,742) = HCF(1988,1246) = HCF(3234,1988) = HCF(8456,3234) .
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Frequently Asked Questions on HCF of 8456, 3234 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 8456, 3234?
Answer: HCF of 8456, 3234 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8456, 3234 using Euclid's Algorithm?
Answer: For arbitrary numbers 8456, 3234 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.