Highest Common Factor of 600, 440, 395 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, 440, 395 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 600, 440, 395 is 5 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, 440, 395 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, 440, 395 is 5.
HCF(600, 440, 395) = 5
HCF of 600, 440, 395 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, 440, 395 is 5.
Highest Common Factor of 600,440,395 is 5
Step 1: Since 600 > 440, we apply the division lemma to 600 and 440, to get
600 = 440 x 1 + 160
Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 160 and 440, to get
440 = 160 x 2 + 120
Step 3: We consider the new divisor 160 and the new remainder 120, and apply the division lemma to get
160 = 120 x 1 + 40
We consider the new divisor 120 and the new remainder 40, and apply the division lemma to get
120 = 40 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 600 and 440 is 40
Notice that 40 = HCF(120,40) = HCF(160,120) = HCF(440,160) = HCF(600,440) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 395 > 40, we apply the division lemma to 395 and 40, to get
395 = 40 x 9 + 35
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 35 and 40, to get
40 = 35 x 1 + 5
Step 3: We consider the new divisor 35 and the new remainder 5, and apply the division lemma to get
35 = 5 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 40 and 395 is 5
Notice that 5 = HCF(35,5) = HCF(40,35) = HCF(395,40) .
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Frequently Asked Questions on HCF of 600, 440, 395 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, 440, 395?
Answer: HCF of 600, 440, 395 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 600, 440, 395 using Euclid's Algorithm?
Answer: For arbitrary numbers 600, 440, 395 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.