Highest Common Factor of 272, 240, 210 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, 240, 210 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 272, 240, 210 is 2 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, 240, 210 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, 240, 210 is 2.
HCF(272, 240, 210) = 2
HCF of 272, 240, 210 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, 240, 210 is 2.
Highest Common Factor of 272,240,210 is 2
Step 1: Since 272 > 240, we apply the division lemma to 272 and 240, to get
272 = 240 x 1 + 32
Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 32 and 240, to get
240 = 32 x 7 + 16
Step 3: We consider the new divisor 32 and the new remainder 16, and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 272 and 240 is 16
Notice that 16 = HCF(32,16) = HCF(240,32) = HCF(272,240) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 210 > 16, we apply the division lemma to 210 and 16, to get
210 = 16 x 13 + 2
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 2 and 16, to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 16 and 210 is 2
Notice that 2 = HCF(16,2) = HCF(210,16) .
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Frequently Asked Questions on HCF of 272, 240, 210 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, 240, 210?
Answer: HCF of 272, 240, 210 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 272, 240, 210 using Euclid's Algorithm?
Answer: For arbitrary numbers 272, 240, 210 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.