Highest Common Factor of 716, 8132 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 716, 8132 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 716, 8132 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 716, 8132 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 716, 8132 is 4.
HCF(716, 8132) = 4
HCF of 716, 8132 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 716, 8132 is 4.
Highest Common Factor of 716,8132 is 4
Step 1: Since 8132 > 716, we apply the division lemma to 8132 and 716, to get
8132 = 716 x 11 + 256
Step 2: Since the reminder 716 ≠ 0, we apply division lemma to 256 and 716, to get
716 = 256 x 2 + 204
Step 3: We consider the new divisor 256 and the new remainder 204, and apply the division lemma to get
256 = 204 x 1 + 52
We consider the new divisor 204 and the new remainder 52,and apply the division lemma to get
204 = 52 x 3 + 48
We consider the new divisor 52 and the new remainder 48,and apply the division lemma to get
52 = 48 x 1 + 4
We consider the new divisor 48 and the new remainder 4,and apply the division lemma to get
48 = 4 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 716 and 8132 is 4
Notice that 4 = HCF(48,4) = HCF(52,48) = HCF(204,52) = HCF(256,204) = HCF(716,256) = HCF(8132,716) .
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Frequently Asked Questions on HCF of 716, 8132 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 716, 8132?
Answer: HCF of 716, 8132 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 716, 8132 using Euclid's Algorithm?
Answer: For arbitrary numbers 716, 8132 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
