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 4705, 3650, 42091 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 4705, 3650, 42091 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 4705, 3650, 42091 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 4705, 3650, 42091 is 1.
HCF(4705, 3650, 42091) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4705, 3650, 42091 is 1.
Step 1: Since 4705 > 3650, we apply the division lemma to 4705 and 3650, to get
4705 = 3650 x 1 + 1055
Step 2: Since the reminder 3650 ≠ 0, we apply division lemma to 1055 and 3650, to get
3650 = 1055 x 3 + 485
Step 3: We consider the new divisor 1055 and the new remainder 485, and apply the division lemma to get
1055 = 485 x 2 + 85
We consider the new divisor 485 and the new remainder 85,and apply the division lemma to get
485 = 85 x 5 + 60
We consider the new divisor 85 and the new remainder 60,and apply the division lemma to get
85 = 60 x 1 + 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 4705 and 3650 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(60,25) = HCF(85,60) = HCF(485,85) = HCF(1055,485) = HCF(3650,1055) = HCF(4705,3650) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42091 > 5, we apply the division lemma to 42091 and 5, to get
42091 = 5 x 8418 + 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 42091 is 1
Notice that 1 = HCF(5,1) = HCF(42091,5) .
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 4705, 3650, 42091?
Answer: HCF of 4705, 3650, 42091 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4705, 3650, 42091 using Euclid's Algorithm?
Answer: For arbitrary numbers 4705, 3650, 42091 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.