Highest Common Factor of 765, 272, 136 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 765, 272, 136 i.e. 17 the largest integer that leaves a remainder zero for all numbers.
HCF of 765, 272, 136 is 17 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 765, 272, 136 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 765, 272, 136 is 17.
HCF(765, 272, 136) = 17
HCF of 765, 272, 136 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 765, 272, 136 is 17.
Highest Common Factor of 765,272,136 is 17
Step 1: Since 765 > 272, we apply the division lemma to 765 and 272, to get
765 = 272 x 2 + 221
Step 2: Since the reminder 272 ≠ 0, we apply division lemma to 221 and 272, to get
272 = 221 x 1 + 51
Step 3: We consider the new divisor 221 and the new remainder 51, and apply the division lemma to get
221 = 51 x 4 + 17
We consider the new divisor 51 and the new remainder 17, and apply the division lemma to get
51 = 17 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 765 and 272 is 17
Notice that 17 = HCF(51,17) = HCF(221,51) = HCF(272,221) = HCF(765,272) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 136 > 17, we apply the division lemma to 136 and 17, to get
136 = 17 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 17 and 136 is 17
Notice that 17 = HCF(136,17) .
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Frequently Asked Questions on HCF of 765, 272, 136 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 765, 272, 136?
Answer: HCF of 765, 272, 136 is 17 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 765, 272, 136 using Euclid's Algorithm?
Answer: For arbitrary numbers 765, 272, 136 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.