Highest Common Factor of 80, 74, 71, 349 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 80, 74, 71, 349 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 80, 74, 71, 349 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 80, 74, 71, 349 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 80, 74, 71, 349 is 1.
HCF(80, 74, 71, 349) = 1
HCF of 80, 74, 71, 349 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 80, 74, 71, 349 is 1.
Highest Common Factor of 80,74,71,349 is 1
Step 1: Since 80 > 74, we apply the division lemma to 80 and 74, to get
80 = 74 x 1 + 6
Step 2: Since the reminder 74 ≠ 0, we apply division lemma to 6 and 74, to get
74 = 6 x 12 + 2
Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 80 and 74 is 2
Notice that 2 = HCF(6,2) = HCF(74,6) = HCF(80,74) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 71 > 2, we apply the division lemma to 71 and 2, to get
71 = 2 x 35 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 71 is 1
Notice that 1 = HCF(2,1) = HCF(71,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 349 > 1, we apply the division lemma to 349 and 1, to get
349 = 1 x 349 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 349 is 1
Notice that 1 = HCF(349,1) .
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Frequently Asked Questions on HCF of 80, 74, 71, 349 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 80, 74, 71, 349?
Answer: HCF of 80, 74, 71, 349 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 80, 74, 71, 349 using Euclid's Algorithm?
Answer: For arbitrary numbers 80, 74, 71, 349 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.