Highest Common Factor of 605, 363, 737 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, 363, 737 i.e. 11 the largest integer that leaves a remainder zero for all numbers.
HCF of 605, 363, 737 is 11 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, 363, 737 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, 363, 737 is 11.
HCF(605, 363, 737) = 11
HCF of 605, 363, 737 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, 363, 737 is 11.
Highest Common Factor of 605,363,737 is 11
Step 1: Since 605 > 363, we apply the division lemma to 605 and 363, to get
605 = 363 x 1 + 242
Step 2: Since the reminder 363 ≠ 0, we apply division lemma to 242 and 363, to get
363 = 242 x 1 + 121
Step 3: We consider the new divisor 242 and the new remainder 121, and apply the division lemma to get
242 = 121 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 121, the HCF of 605 and 363 is 121
Notice that 121 = HCF(242,121) = HCF(363,242) = HCF(605,363) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 737 > 121, we apply the division lemma to 737 and 121, to get
737 = 121 x 6 + 11
Step 2: Since the reminder 121 ≠ 0, we apply division lemma to 11 and 121, to get
121 = 11 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 121 and 737 is 11
Notice that 11 = HCF(121,11) = HCF(737,121) .
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Frequently Asked Questions on HCF of 605, 363, 737 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, 363, 737?
Answer: HCF of 605, 363, 737 is 11 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 605, 363, 737 using Euclid's Algorithm?
Answer: For arbitrary numbers 605, 363, 737 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.