Highest Common Factor of 491, 7984 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 491, 7984 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 491, 7984 is 1 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 491, 7984 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 491, 7984 is 1.
HCF(491, 7984) = 1
HCF of 491, 7984 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 491, 7984 is 1.
Highest Common Factor of 491,7984 is 1
Step 1: Since 7984 > 491, we apply the division lemma to 7984 and 491, to get
7984 = 491 x 16 + 128
Step 2: Since the reminder 491 ≠ 0, we apply division lemma to 128 and 491, to get
491 = 128 x 3 + 107
Step 3: We consider the new divisor 128 and the new remainder 107, and apply the division lemma to get
128 = 107 x 1 + 21
We consider the new divisor 107 and the new remainder 21,and apply the division lemma to get
107 = 21 x 5 + 2
We consider the new divisor 21 and the new remainder 2,and apply the division lemma to get
21 = 2 x 10 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 491 and 7984 is 1
Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(107,21) = HCF(128,107) = HCF(491,128) = HCF(7984,491) .
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Frequently Asked Questions on HCF of 491, 7984 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 491, 7984?
Answer: HCF of 491, 7984 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 491, 7984 using Euclid's Algorithm?
Answer: For arbitrary numbers 491, 7984 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.