Highest Common Factor of 370, 574, 80 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 370, 574, 80 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 370, 574, 80 is 2 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 370, 574, 80 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 370, 574, 80 is 2.
HCF(370, 574, 80) = 2
HCF of 370, 574, 80 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 370, 574, 80 is 2.
Highest Common Factor of 370,574,80 is 2
Step 1: Since 574 > 370, we apply the division lemma to 574 and 370, to get
574 = 370 x 1 + 204
Step 2: Since the reminder 370 ≠ 0, we apply division lemma to 204 and 370, to get
370 = 204 x 1 + 166
Step 3: We consider the new divisor 204 and the new remainder 166, and apply the division lemma to get
204 = 166 x 1 + 38
We consider the new divisor 166 and the new remainder 38,and apply the division lemma to get
166 = 38 x 4 + 14
We consider the new divisor 38 and the new remainder 14,and apply the division lemma to get
38 = 14 x 2 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 370 and 574 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(38,14) = HCF(166,38) = HCF(204,166) = HCF(370,204) = HCF(574,370) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 80 > 2, we apply the division lemma to 80 and 2, to get
80 = 2 x 40 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 80 is 2
Notice that 2 = HCF(80,2) .
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Frequently Asked Questions on HCF of 370, 574, 80 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 370, 574, 80?
Answer: HCF of 370, 574, 80 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 370, 574, 80 using Euclid's Algorithm?
Answer: For arbitrary numbers 370, 574, 80 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.