Highest Common Factor of 548, 345, 14, 371 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 548, 345, 14, 371 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 548, 345, 14, 371 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 548, 345, 14, 371 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 548, 345, 14, 371 is 1.
HCF(548, 345, 14, 371) = 1
HCF of 548, 345, 14, 371 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 548, 345, 14, 371 is 1.
Highest Common Factor of 548,345,14,371 is 1
Step 1: Since 548 > 345, we apply the division lemma to 548 and 345, to get
548 = 345 x 1 + 203
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 203 and 345, to get
345 = 203 x 1 + 142
Step 3: We consider the new divisor 203 and the new remainder 142, and apply the division lemma to get
203 = 142 x 1 + 61
We consider the new divisor 142 and the new remainder 61,and apply the division lemma to get
142 = 61 x 2 + 20
We consider the new divisor 61 and the new remainder 20,and apply the division lemma to get
61 = 20 x 3 + 1
We consider the new divisor 20 and the new remainder 1,and apply the division lemma to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 548 and 345 is 1
Notice that 1 = HCF(20,1) = HCF(61,20) = HCF(142,61) = HCF(203,142) = HCF(345,203) = HCF(548,345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 14 > 1, we apply the division lemma to 14 and 1, to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 14 is 1
Notice that 1 = HCF(14,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 371 > 1, we apply the division lemma to 371 and 1, to get
371 = 1 x 371 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 371 is 1
Notice that 1 = HCF(371,1) .
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Frequently Asked Questions on HCF of 548, 345, 14, 371 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 548, 345, 14, 371?
Answer: HCF of 548, 345, 14, 371 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 548, 345, 14, 371 using Euclid's Algorithm?
Answer: For arbitrary numbers 548, 345, 14, 371 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.