Highest Common Factor of 590, 472, 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 590, 472, 340 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 590, 472, 340 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 590, 472, 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 590, 472, 340 is 2.
HCF(590, 472, 340) = 2
HCF of 590, 472, 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 590, 472, 340 is 2.
Highest Common Factor of 590,472,340 is 2
Step 1: Since 590 > 472, we apply the division lemma to 590 and 472, to get
590 = 472 x 1 + 118
Step 2: Since the reminder 472 ≠ 0, we apply division lemma to 118 and 472, to get
472 = 118 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 118, the HCF of 590 and 472 is 118
Notice that 118 = HCF(472,118) = HCF(590,472) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 340 > 118, we apply the division lemma to 340 and 118, to get
340 = 118 x 2 + 104
Step 2: Since the reminder 118 ≠ 0, we apply division lemma to 104 and 118, to get
118 = 104 x 1 + 14
Step 3: We consider the new divisor 104 and the new remainder 14, and apply the division lemma to get
104 = 14 x 7 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 2
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 118 and 340 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(104,14) = HCF(118,104) = HCF(340,118) .
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Frequently Asked Questions on HCF of 590, 472, 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 590, 472, 340?
Answer: HCF of 590, 472, 340 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 590, 472, 340 using Euclid's Algorithm?
Answer: For arbitrary numbers 590, 472, 340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.