Highest Common Factor of 824, 9608, 2324 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 824, 9608, 2324 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 824, 9608, 2324 is 4 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 824, 9608, 2324 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 824, 9608, 2324 is 4.
HCF(824, 9608, 2324) = 4
HCF of 824, 9608, 2324 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 824, 9608, 2324 is 4.
Highest Common Factor of 824,9608,2324 is 4
Step 1: Since 9608 > 824, we apply the division lemma to 9608 and 824, to get
9608 = 824 x 11 + 544
Step 2: Since the reminder 824 ≠ 0, we apply division lemma to 544 and 824, to get
824 = 544 x 1 + 280
Step 3: We consider the new divisor 544 and the new remainder 280, and apply the division lemma to get
544 = 280 x 1 + 264
We consider the new divisor 280 and the new remainder 264,and apply the division lemma to get
280 = 264 x 1 + 16
We consider the new divisor 264 and the new remainder 16,and apply the division lemma to get
264 = 16 x 16 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 824 and 9608 is 8
Notice that 8 = HCF(16,8) = HCF(264,16) = HCF(280,264) = HCF(544,280) = HCF(824,544) = HCF(9608,824) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2324 > 8, we apply the division lemma to 2324 and 8, to get
2324 = 8 x 290 + 4
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 4 and 8, to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 8 and 2324 is 4
Notice that 4 = HCF(8,4) = HCF(2324,8) .
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Frequently Asked Questions on HCF of 824, 9608, 2324 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 824, 9608, 2324?
Answer: HCF of 824, 9608, 2324 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 824, 9608, 2324 using Euclid's Algorithm?
Answer: For arbitrary numbers 824, 9608, 2324 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.