Highest Common Factor of 600, 382, 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 600, 382, 340 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 600, 382, 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 600, 382, 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 600, 382, 340 is 2.
HCF(600, 382, 340) = 2
HCF of 600, 382, 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 600, 382, 340 is 2.
Highest Common Factor of 600,382,340 is 2
Step 1: Since 600 > 382, we apply the division lemma to 600 and 382, to get
600 = 382 x 1 + 218
Step 2: Since the reminder 382 ≠ 0, we apply division lemma to 218 and 382, to get
382 = 218 x 1 + 164
Step 3: We consider the new divisor 218 and the new remainder 164, and apply the division lemma to get
218 = 164 x 1 + 54
We consider the new divisor 164 and the new remainder 54,and apply the division lemma to get
164 = 54 x 3 + 2
We consider the new divisor 54 and the new remainder 2,and apply the division lemma to get
54 = 2 x 27 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 600 and 382 is 2
Notice that 2 = HCF(54,2) = HCF(164,54) = HCF(218,164) = HCF(382,218) = HCF(600,382) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 340 > 2, we apply the division lemma to 340 and 2, to get
340 = 2 x 170 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 340 is 2
Notice that 2 = HCF(340,2) .
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Frequently Asked Questions on HCF of 600, 382, 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 600, 382, 340?
Answer: HCF of 600, 382, 340 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 600, 382, 340 using Euclid's Algorithm?
Answer: For arbitrary numbers 600, 382, 340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
