Highest Common Factor of 7749, 9734 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 7749, 9734 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7749, 9734 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 7749, 9734 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 7749, 9734 is 1.
HCF(7749, 9734) = 1
HCF of 7749, 9734 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7749, 9734 is 1.
Highest Common Factor of 7749,9734 is 1
Step 1: Since 9734 > 7749, we apply the division lemma to 9734 and 7749, to get
9734 = 7749 x 1 + 1985
Step 2: Since the reminder 7749 ≠ 0, we apply division lemma to 1985 and 7749, to get
7749 = 1985 x 3 + 1794
Step 3: We consider the new divisor 1985 and the new remainder 1794, and apply the division lemma to get
1985 = 1794 x 1 + 191
We consider the new divisor 1794 and the new remainder 191,and apply the division lemma to get
1794 = 191 x 9 + 75
We consider the new divisor 191 and the new remainder 75,and apply the division lemma to get
191 = 75 x 2 + 41
We consider the new divisor 75 and the new remainder 41,and apply the division lemma to get
75 = 41 x 1 + 34
We consider the new divisor 41 and the new remainder 34,and apply the division lemma to get
41 = 34 x 1 + 7
We consider the new divisor 34 and the new remainder 7,and apply the division lemma to get
34 = 7 x 4 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7749 and 9734 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(34,7) = HCF(41,34) = HCF(75,41) = HCF(191,75) = HCF(1794,191) = HCF(1985,1794) = HCF(7749,1985) = HCF(9734,7749) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 7749, 9734 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 7749, 9734?
Answer: HCF of 7749, 9734 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7749, 9734 using Euclid's Algorithm?
Answer: For arbitrary numbers 7749, 9734 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.