Highest Common Factor of 665, 136, 268 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 665, 136, 268 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 665, 136, 268 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 665, 136, 268 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 665, 136, 268 is 1.
HCF(665, 136, 268) = 1
HCF of 665, 136, 268 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 665, 136, 268 is 1.
Highest Common Factor of 665,136,268 is 1
Step 1: Since 665 > 136, we apply the division lemma to 665 and 136, to get
665 = 136 x 4 + 121
Step 2: Since the reminder 136 ≠ 0, we apply division lemma to 121 and 136, to get
136 = 121 x 1 + 15
Step 3: We consider the new divisor 121 and the new remainder 15, and apply the division lemma to get
121 = 15 x 8 + 1
We consider the new divisor 15 and the new remainder 1, and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 665 and 136 is 1
Notice that 1 = HCF(15,1) = HCF(121,15) = HCF(136,121) = HCF(665,136) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 268 > 1, we apply the division lemma to 268 and 1, to get
268 = 1 x 268 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 268 is 1
Notice that 1 = HCF(268,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 665, 136, 268 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 665, 136, 268?
Answer: HCF of 665, 136, 268 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 665, 136, 268 using Euclid's Algorithm?
Answer: For arbitrary numbers 665, 136, 268 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.