Highest Common Factor of 1405, 2698 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 1405, 2698 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1405, 2698 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 1405, 2698 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 1405, 2698 is 1.
HCF(1405, 2698) = 1
HCF of 1405, 2698 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1405, 2698 is 1.
Highest Common Factor of 1405,2698 is 1
Step 1: Since 2698 > 1405, we apply the division lemma to 2698 and 1405, to get
2698 = 1405 x 1 + 1293
Step 2: Since the reminder 1405 ≠ 0, we apply division lemma to 1293 and 1405, to get
1405 = 1293 x 1 + 112
Step 3: We consider the new divisor 1293 and the new remainder 112, and apply the division lemma to get
1293 = 112 x 11 + 61
We consider the new divisor 112 and the new remainder 61,and apply the division lemma to get
112 = 61 x 1 + 51
We consider the new divisor 61 and the new remainder 51,and apply the division lemma to get
61 = 51 x 1 + 10
We consider the new divisor 51 and the new remainder 10,and apply the division lemma to get
51 = 10 x 5 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1405 and 2698 is 1
Notice that 1 = HCF(10,1) = HCF(51,10) = HCF(61,51) = HCF(112,61) = HCF(1293,112) = HCF(1405,1293) = HCF(2698,1405) .
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Frequently Asked Questions on HCF of 1405, 2698 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 1405, 2698?
Answer: HCF of 1405, 2698 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1405, 2698 using Euclid's Algorithm?
Answer: For arbitrary numbers 1405, 2698 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.