Highest Common Factor of 4184, 8000 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 4184, 8000 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 4184, 8000 is 8 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 4184, 8000 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 4184, 8000 is 8.
HCF(4184, 8000) = 8
HCF of 4184, 8000 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4184, 8000 is 8.
Highest Common Factor of 4184,8000 is 8
Step 1: Since 8000 > 4184, we apply the division lemma to 8000 and 4184, to get
8000 = 4184 x 1 + 3816
Step 2: Since the reminder 4184 ≠ 0, we apply division lemma to 3816 and 4184, to get
4184 = 3816 x 1 + 368
Step 3: We consider the new divisor 3816 and the new remainder 368, and apply the division lemma to get
3816 = 368 x 10 + 136
We consider the new divisor 368 and the new remainder 136,and apply the division lemma to get
368 = 136 x 2 + 96
We consider the new divisor 136 and the new remainder 96,and apply the division lemma to get
136 = 96 x 1 + 40
We consider the new divisor 96 and the new remainder 40,and apply the division lemma to get
96 = 40 x 2 + 16
We consider the new divisor 40 and the new remainder 16,and apply the division lemma to get
40 = 16 x 2 + 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 4184 and 8000 is 8
Notice that 8 = HCF(16,8) = HCF(40,16) = HCF(96,40) = HCF(136,96) = HCF(368,136) = HCF(3816,368) = HCF(4184,3816) = HCF(8000,4184) .
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Frequently Asked Questions on HCF of 4184, 8000 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 4184, 8000?
Answer: HCF of 4184, 8000 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4184, 8000 using Euclid's Algorithm?
Answer: For arbitrary numbers 4184, 8000 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.