Highest Common Factor of 9741, 754 using Euclid's algorithm
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 9741, 754 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9741, 754 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 9741, 754 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 9741, 754 is 1.
HCF(9741, 754) = 1
HCF of 9741, 754 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9741, 754 is 1.
Highest Common Factor of 9741,754 is 1
Step 1: Since 9741 > 754, we apply the division lemma to 9741 and 754, to get
9741 = 754 x 12 + 693
Step 2: Since the reminder 754 ≠ 0, we apply division lemma to 693 and 754, to get
754 = 693 x 1 + 61
Step 3: We consider the new divisor 693 and the new remainder 61, and apply the division lemma to get
693 = 61 x 11 + 22
We consider the new divisor 61 and the new remainder 22,and apply the division lemma to get
61 = 22 x 2 + 17
We consider the new divisor 22 and the new remainder 17,and apply the division lemma to get
22 = 17 x 1 + 5
We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 9741 and 754 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(61,22) = HCF(693,61) = HCF(754,693) = HCF(9741,754) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 9741, 754 using Euclid's Algorithm
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 9741, 754?
Answer: HCF of 9741, 754 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9741, 754 using Euclid's Algorithm?
Answer: For arbitrary numbers 9741, 754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.