Highest Common Factor of 5688, 9174 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 5688, 9174 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 5688, 9174 is 6 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 5688, 9174 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 5688, 9174 is 6.
HCF(5688, 9174) = 6
HCF of 5688, 9174 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5688, 9174 is 6.
Highest Common Factor of 5688,9174 is 6
Step 1: Since 9174 > 5688, we apply the division lemma to 9174 and 5688, to get
9174 = 5688 x 1 + 3486
Step 2: Since the reminder 5688 ≠ 0, we apply division lemma to 3486 and 5688, to get
5688 = 3486 x 1 + 2202
Step 3: We consider the new divisor 3486 and the new remainder 2202, and apply the division lemma to get
3486 = 2202 x 1 + 1284
We consider the new divisor 2202 and the new remainder 1284,and apply the division lemma to get
2202 = 1284 x 1 + 918
We consider the new divisor 1284 and the new remainder 918,and apply the division lemma to get
1284 = 918 x 1 + 366
We consider the new divisor 918 and the new remainder 366,and apply the division lemma to get
918 = 366 x 2 + 186
We consider the new divisor 366 and the new remainder 186,and apply the division lemma to get
366 = 186 x 1 + 180
We consider the new divisor 186 and the new remainder 180,and apply the division lemma to get
186 = 180 x 1 + 6
We consider the new divisor 180 and the new remainder 6,and apply the division lemma to get
180 = 6 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 5688 and 9174 is 6
Notice that 6 = HCF(180,6) = HCF(186,180) = HCF(366,186) = HCF(918,366) = HCF(1284,918) = HCF(2202,1284) = HCF(3486,2202) = HCF(5688,3486) = HCF(9174,5688) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 5688, 9174 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 5688, 9174?
Answer: HCF of 5688, 9174 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5688, 9174 using Euclid's Algorithm?
Answer: For arbitrary numbers 5688, 9174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
