Highest Common Factor of 372, 589, 340 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 372, 589, 340 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 372, 589, 340 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 372, 589, 340 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 372, 589, 340 is 1.
HCF(372, 589, 340) = 1
HCF of 372, 589, 340 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 372, 589, 340 is 1.
Highest Common Factor of 372,589,340 is 1
Step 1: Since 589 > 372, we apply the division lemma to 589 and 372, to get
589 = 372 x 1 + 217
Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 217 and 372, to get
372 = 217 x 1 + 155
Step 3: We consider the new divisor 217 and the new remainder 155, and apply the division lemma to get
217 = 155 x 1 + 62
We consider the new divisor 155 and the new remainder 62,and apply the division lemma to get
155 = 62 x 2 + 31
We consider the new divisor 62 and the new remainder 31,and apply the division lemma to get
62 = 31 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 31, the HCF of 372 and 589 is 31
Notice that 31 = HCF(62,31) = HCF(155,62) = HCF(217,155) = HCF(372,217) = HCF(589,372) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 340 > 31, we apply the division lemma to 340 and 31, to get
340 = 31 x 10 + 30
Step 2: Since the reminder 31 ≠ 0, we apply division lemma to 30 and 31, to get
31 = 30 x 1 + 1
Step 3: We consider the new divisor 30 and the new remainder 1, and apply the division lemma to get
30 = 1 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 31 and 340 is 1
Notice that 1 = HCF(30,1) = HCF(31,30) = HCF(340,31) .
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Frequently Asked Questions on HCF of 372, 589, 340 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 372, 589, 340?
Answer: HCF of 372, 589, 340 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 372, 589, 340 using Euclid's Algorithm?
Answer: For arbitrary numbers 372, 589, 340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
