Highest Common Factor of 66, 86, 364, 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 66, 86, 364, 272 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 66, 86, 364, 272 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 66, 86, 364, 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 66, 86, 364, 272 is 2.
HCF(66, 86, 364, 272) = 2
HCF of 66, 86, 364, 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 66, 86, 364, 272 is 2.
Highest Common Factor of 66,86,364,272 is 2
Step 1: Since 86 > 66, we apply the division lemma to 86 and 66, to get
86 = 66 x 1 + 20
Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 20 and 66, to get
66 = 20 x 3 + 6
Step 3: We consider the new divisor 20 and the new remainder 6, and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 66 and 86 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(66,20) = HCF(86,66) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 364 > 2, we apply the division lemma to 364 and 2, to get
364 = 2 x 182 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 364 is 2
Notice that 2 = HCF(364,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 272 > 2, we apply the division lemma to 272 and 2, to get
272 = 2 x 136 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 272 is 2
Notice that 2 = HCF(272,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 66, 86, 364, 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 66, 86, 364, 272?
Answer: HCF of 66, 86, 364, 272 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 66, 86, 364, 272 using Euclid's Algorithm?
Answer: For arbitrary numbers 66, 86, 364, 272 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.