Highest Common Factor of 735, 906, 272 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 735, 906, 272 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 735, 906, 272 is 1 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 735, 906, 272 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 735, 906, 272 is 1.
HCF(735, 906, 272) = 1
HCF of 735, 906, 272 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 735, 906, 272 is 1.
Highest Common Factor of 735,906,272 is 1
Step 1: Since 906 > 735, we apply the division lemma to 906 and 735, to get
906 = 735 x 1 + 171
Step 2: Since the reminder 735 ≠ 0, we apply division lemma to 171 and 735, to get
735 = 171 x 4 + 51
Step 3: We consider the new divisor 171 and the new remainder 51, and apply the division lemma to get
171 = 51 x 3 + 18
We consider the new divisor 51 and the new remainder 18,and apply the division lemma to get
51 = 18 x 2 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 735 and 906 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(51,18) = HCF(171,51) = HCF(735,171) = HCF(906,735) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 272 > 3, we apply the division lemma to 272 and 3, to get
272 = 3 x 90 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 272 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(272,3) .
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Frequently Asked Questions on HCF of 735, 906, 272 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 735, 906, 272?
Answer: HCF of 735, 906, 272 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 735, 906, 272 using Euclid's Algorithm?
Answer: For arbitrary numbers 735, 906, 272 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
