Highest Common Factor of 261, 416, 35 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 261, 416, 35 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 261, 416, 35 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 261, 416, 35 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 261, 416, 35 is 1.
HCF(261, 416, 35) = 1
HCF of 261, 416, 35 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 261, 416, 35 is 1.
Highest Common Factor of 261,416,35 is 1
Step 1: Since 416 > 261, we apply the division lemma to 416 and 261, to get
416 = 261 x 1 + 155
Step 2: Since the reminder 261 ≠ 0, we apply division lemma to 155 and 261, to get
261 = 155 x 1 + 106
Step 3: We consider the new divisor 155 and the new remainder 106, and apply the division lemma to get
155 = 106 x 1 + 49
We consider the new divisor 106 and the new remainder 49,and apply the division lemma to get
106 = 49 x 2 + 8
We consider the new divisor 49 and the new remainder 8,and apply the division lemma to get
49 = 8 x 6 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 261 and 416 is 1
Notice that 1 = HCF(8,1) = HCF(49,8) = HCF(106,49) = HCF(155,106) = HCF(261,155) = HCF(416,261) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 35 > 1, we apply the division lemma to 35 and 1, to get
35 = 1 x 35 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 35 is 1
Notice that 1 = HCF(35,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 261, 416, 35 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 261, 416, 35?
Answer: HCF of 261, 416, 35 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 261, 416, 35 using Euclid's Algorithm?
Answer: For arbitrary numbers 261, 416, 35 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.