Highest Common Factor of 324, 854 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 324, 854 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 324, 854 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 324, 854 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 324, 854 is 2.
HCF(324, 854) = 2
HCF of 324, 854 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 324, 854 is 2.
Highest Common Factor of 324,854 is 2
Step 1: Since 854 > 324, we apply the division lemma to 854 and 324, to get
854 = 324 x 2 + 206
Step 2: Since the reminder 324 ≠ 0, we apply division lemma to 206 and 324, to get
324 = 206 x 1 + 118
Step 3: We consider the new divisor 206 and the new remainder 118, and apply the division lemma to get
206 = 118 x 1 + 88
We consider the new divisor 118 and the new remainder 88,and apply the division lemma to get
118 = 88 x 1 + 30
We consider the new divisor 88 and the new remainder 30,and apply the division lemma to get
88 = 30 x 2 + 28
We consider the new divisor 30 and the new remainder 28,and apply the division lemma to get
30 = 28 x 1 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 324 and 854 is 2
Notice that 2 = HCF(28,2) = HCF(30,28) = HCF(88,30) = HCF(118,88) = HCF(206,118) = HCF(324,206) = HCF(854,324) .
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Frequently Asked Questions on HCF of 324, 854 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 324, 854?
Answer: HCF of 324, 854 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 324, 854 using Euclid's Algorithm?
Answer: For arbitrary numbers 324, 854 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.