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 1908, 7747 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1908, 7747 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 1908, 7747 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 1908, 7747 is 1.
HCF(1908, 7747) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1908, 7747 is 1.
Step 1: Since 7747 > 1908, we apply the division lemma to 7747 and 1908, to get
7747 = 1908 x 4 + 115
Step 2: Since the reminder 1908 ≠ 0, we apply division lemma to 115 and 1908, to get
1908 = 115 x 16 + 68
Step 3: We consider the new divisor 115 and the new remainder 68, and apply the division lemma to get
115 = 68 x 1 + 47
We consider the new divisor 68 and the new remainder 47,and apply the division lemma to get
68 = 47 x 1 + 21
We consider the new divisor 47 and the new remainder 21,and apply the division lemma to get
47 = 21 x 2 + 5
We consider the new divisor 21 and the new remainder 5,and apply the division lemma to get
21 = 5 x 4 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma 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 1908 and 7747 is 1
Notice that 1 = HCF(5,1) = HCF(21,5) = HCF(47,21) = HCF(68,47) = HCF(115,68) = HCF(1908,115) = HCF(7747,1908) .
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 1908, 7747?
Answer: HCF of 1908, 7747 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1908, 7747 using Euclid's Algorithm?
Answer: For arbitrary numbers 1908, 7747 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.