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, 413, 94 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 261, 413, 94 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, 413, 94 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, 413, 94 is 1.
HCF(261, 413, 94) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 261, 413, 94 is 1.
Step 1: Since 413 > 261, we apply the division lemma to 413 and 261, to get
413 = 261 x 1 + 152
Step 2: Since the reminder 261 ≠ 0, we apply division lemma to 152 and 261, to get
261 = 152 x 1 + 109
Step 3: We consider the new divisor 152 and the new remainder 109, and apply the division lemma to get
152 = 109 x 1 + 43
We consider the new divisor 109 and the new remainder 43,and apply the division lemma to get
109 = 43 x 2 + 23
We consider the new divisor 43 and the new remainder 23,and apply the division lemma to get
43 = 23 x 1 + 20
We consider the new divisor 23 and the new remainder 20,and apply the division lemma to get
23 = 20 x 1 + 3
We consider the new divisor 20 and the new remainder 3,and apply the division lemma to get
20 = 3 x 6 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 261 and 413 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(23,20) = HCF(43,23) = HCF(109,43) = HCF(152,109) = HCF(261,152) = HCF(413,261) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 94 > 1, we apply the division lemma to 94 and 1, to get
94 = 1 x 94 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 94 is 1
Notice that 1 = HCF(94,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 413, 94?
Answer: HCF of 261, 413, 94 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 261, 413, 94 using Euclid's Algorithm?
Answer: For arbitrary numbers 261, 413, 94 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.