Highest Common Factor of 272, 384, 508, 765 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 272, 384, 508, 765 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 272, 384, 508, 765 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 272, 384, 508, 765 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 272, 384, 508, 765 is 1.
HCF(272, 384, 508, 765) = 1
HCF of 272, 384, 508, 765 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 272, 384, 508, 765 is 1.
Highest Common Factor of 272,384,508,765 is 1
Step 1: Since 384 > 272, we apply the division lemma to 384 and 272, to get
384 = 272 x 1 + 112
Step 2: Since the reminder 272 ≠ 0, we apply division lemma to 112 and 272, to get
272 = 112 x 2 + 48
Step 3: We consider the new divisor 112 and the new remainder 48, and apply the division lemma to get
112 = 48 x 2 + 16
We consider the new divisor 48 and the new remainder 16, and apply the division lemma to get
48 = 16 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 272 and 384 is 16
Notice that 16 = HCF(48,16) = HCF(112,48) = HCF(272,112) = HCF(384,272) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 508 > 16, we apply the division lemma to 508 and 16, to get
508 = 16 x 31 + 12
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 12 and 16, to get
16 = 12 x 1 + 4
Step 3: We consider the new divisor 12 and the new remainder 4, and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 16 and 508 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(508,16) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 765 > 4, we apply the division lemma to 765 and 4, to get
765 = 4 x 191 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 765 is 1
Notice that 1 = HCF(4,1) = HCF(765,4) .
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Frequently Asked Questions on HCF of 272, 384, 508, 765 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 272, 384, 508, 765?
Answer: HCF of 272, 384, 508, 765 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 272, 384, 508, 765 using Euclid's Algorithm?
Answer: For arbitrary numbers 272, 384, 508, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.