Highest Common Factor of 605, 355, 440 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 605, 355, 440 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 605, 355, 440 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 605, 355, 440 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 605, 355, 440 is 5.
HCF(605, 355, 440) = 5
HCF of 605, 355, 440 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 605, 355, 440 is 5.
Highest Common Factor of 605,355,440 is 5
Step 1: Since 605 > 355, we apply the division lemma to 605 and 355, to get
605 = 355 x 1 + 250
Step 2: Since the reminder 355 ≠ 0, we apply division lemma to 250 and 355, to get
355 = 250 x 1 + 105
Step 3: We consider the new divisor 250 and the new remainder 105, and apply the division lemma to get
250 = 105 x 2 + 40
We consider the new divisor 105 and the new remainder 40,and apply the division lemma to get
105 = 40 x 2 + 25
We consider the new divisor 40 and the new remainder 25,and apply the division lemma to get
40 = 25 x 1 + 15
We consider the new divisor 25 and the new remainder 15,and apply the division lemma to get
25 = 15 x 1 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 605 and 355 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(40,25) = HCF(105,40) = HCF(250,105) = HCF(355,250) = HCF(605,355) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 440 > 5, we apply the division lemma to 440 and 5, to get
440 = 5 x 88 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 440 is 5
Notice that 5 = HCF(440,5) .
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Frequently Asked Questions on HCF of 605, 355, 440 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 605, 355, 440?
Answer: HCF of 605, 355, 440 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 605, 355, 440 using Euclid's Algorithm?
Answer: For arbitrary numbers 605, 355, 440 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
