Highest Common Factor of 272, 2340 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, 2340 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 272, 2340 is 4 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, 2340 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, 2340 is 4.
HCF(272, 2340) = 4
HCF of 272, 2340 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, 2340 is 4.
Highest Common Factor of 272,2340 is 4
Step 1: Since 2340 > 272, we apply the division lemma to 2340 and 272, to get
2340 = 272 x 8 + 164
Step 2: Since the reminder 272 ≠ 0, we apply division lemma to 164 and 272, to get
272 = 164 x 1 + 108
Step 3: We consider the new divisor 164 and the new remainder 108, and apply the division lemma to get
164 = 108 x 1 + 56
We consider the new divisor 108 and the new remainder 56,and apply the division lemma to get
108 = 56 x 1 + 52
We consider the new divisor 56 and the new remainder 52,and apply the division lemma to get
56 = 52 x 1 + 4
We consider the new divisor 52 and the new remainder 4,and apply the division lemma to get
52 = 4 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 272 and 2340 is 4
Notice that 4 = HCF(52,4) = HCF(56,52) = HCF(108,56) = HCF(164,108) = HCF(272,164) = HCF(2340,272) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 272, 2340 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, 2340?
Answer: HCF of 272, 2340 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 272, 2340 using Euclid's Algorithm?
Answer: For arbitrary numbers 272, 2340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.