Highest Common Factor of 1967, 8491, 78292 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 1967, 8491, 78292 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1967, 8491, 78292 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 1967, 8491, 78292 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 1967, 8491, 78292 is 1.
HCF(1967, 8491, 78292) = 1
HCF of 1967, 8491, 78292 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1967, 8491, 78292 is 1.
Highest Common Factor of 1967,8491,78292 is 1
Step 1: Since 8491 > 1967, we apply the division lemma to 8491 and 1967, to get
8491 = 1967 x 4 + 623
Step 2: Since the reminder 1967 ≠ 0, we apply division lemma to 623 and 1967, to get
1967 = 623 x 3 + 98
Step 3: We consider the new divisor 623 and the new remainder 98, and apply the division lemma to get
623 = 98 x 6 + 35
We consider the new divisor 98 and the new remainder 35,and apply the division lemma to get
98 = 35 x 2 + 28
We consider the new divisor 35 and the new remainder 28,and apply the division lemma to get
35 = 28 x 1 + 7
We consider the new divisor 28 and the new remainder 7,and apply the division lemma to get
28 = 7 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 1967 and 8491 is 7
Notice that 7 = HCF(28,7) = HCF(35,28) = HCF(98,35) = HCF(623,98) = HCF(1967,623) = HCF(8491,1967) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 78292 > 7, we apply the division lemma to 78292 and 7, to get
78292 = 7 x 11184 + 4
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 4 and 7, to get
7 = 4 x 1 + 3
Step 3: We consider the new divisor 4 and the new remainder 3, and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 78292 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(78292,7) .
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Frequently Asked Questions on HCF of 1967, 8491, 78292 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 1967, 8491, 78292?
Answer: HCF of 1967, 8491, 78292 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1967, 8491, 78292 using Euclid's Algorithm?
Answer: For arbitrary numbers 1967, 8491, 78292 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
