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 1850, 9071, 13707 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1850, 9071, 13707 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 1850, 9071, 13707 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 1850, 9071, 13707 is 1.
HCF(1850, 9071, 13707) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1850, 9071, 13707 is 1.
Step 1: Since 9071 > 1850, we apply the division lemma to 9071 and 1850, to get
9071 = 1850 x 4 + 1671
Step 2: Since the reminder 1850 ≠ 0, we apply division lemma to 1671 and 1850, to get
1850 = 1671 x 1 + 179
Step 3: We consider the new divisor 1671 and the new remainder 179, and apply the division lemma to get
1671 = 179 x 9 + 60
We consider the new divisor 179 and the new remainder 60,and apply the division lemma to get
179 = 60 x 2 + 59
We consider the new divisor 60 and the new remainder 59,and apply the division lemma to get
60 = 59 x 1 + 1
We consider the new divisor 59 and the new remainder 1,and apply the division lemma to get
59 = 1 x 59 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1850 and 9071 is 1
Notice that 1 = HCF(59,1) = HCF(60,59) = HCF(179,60) = HCF(1671,179) = HCF(1850,1671) = HCF(9071,1850) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 13707 > 1, we apply the division lemma to 13707 and 1, to get
13707 = 1 x 13707 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 13707 is 1
Notice that 1 = HCF(13707,1) .
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 1850, 9071, 13707?
Answer: HCF of 1850, 9071, 13707 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1850, 9071, 13707 using Euclid's Algorithm?
Answer: For arbitrary numbers 1850, 9071, 13707 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.