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 265, 735, 301, 841 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 265, 735, 301, 841 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 265, 735, 301, 841 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 265, 735, 301, 841 is 1.
HCF(265, 735, 301, 841) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 265, 735, 301, 841 is 1.
Step 1: Since 735 > 265, we apply the division lemma to 735 and 265, to get
735 = 265 x 2 + 205
Step 2: Since the reminder 265 ≠ 0, we apply division lemma to 205 and 265, to get
265 = 205 x 1 + 60
Step 3: We consider the new divisor 205 and the new remainder 60, and apply the division lemma to get
205 = 60 x 3 + 25
We consider the new divisor 60 and the new remainder 25,and apply the division lemma to get
60 = 25 x 2 + 10
We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get
25 = 10 x 2 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 265 and 735 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(60,25) = HCF(205,60) = HCF(265,205) = HCF(735,265) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 301 > 5, we apply the division lemma to 301 and 5, to get
301 = 5 x 60 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 301 is 1
Notice that 1 = HCF(5,1) = HCF(301,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 841 > 1, we apply the division lemma to 841 and 1, to get
841 = 1 x 841 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 841 is 1
Notice that 1 = HCF(841,1) .
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 265, 735, 301, 841?
Answer: HCF of 265, 735, 301, 841 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 265, 735, 301, 841 using Euclid's Algorithm?
Answer: For arbitrary numbers 265, 735, 301, 841 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.