Highest Common Factor of 1704, 5906 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 1704, 5906 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1704, 5906 is 2 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 1704, 5906 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 1704, 5906 is 2.
HCF(1704, 5906) = 2
HCF of 1704, 5906 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1704, 5906 is 2.
Highest Common Factor of 1704,5906 is 2
Step 1: Since 5906 > 1704, we apply the division lemma to 5906 and 1704, to get
5906 = 1704 x 3 + 794
Step 2: Since the reminder 1704 ≠ 0, we apply division lemma to 794 and 1704, to get
1704 = 794 x 2 + 116
Step 3: We consider the new divisor 794 and the new remainder 116, and apply the division lemma to get
794 = 116 x 6 + 98
We consider the new divisor 116 and the new remainder 98,and apply the division lemma to get
116 = 98 x 1 + 18
We consider the new divisor 98 and the new remainder 18,and apply the division lemma to get
98 = 18 x 5 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1704 and 5906 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(98,18) = HCF(116,98) = HCF(794,116) = HCF(1704,794) = HCF(5906,1704) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 1704, 5906 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 1704, 5906?
Answer: HCF of 1704, 5906 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1704, 5906 using Euclid's Algorithm?
Answer: For arbitrary numbers 1704, 5906 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
