Highest Common Factor of 1702, 7424 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 1702, 7424 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1702, 7424 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 1702, 7424 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 1702, 7424 is 2.
HCF(1702, 7424) = 2
HCF of 1702, 7424 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1702, 7424 is 2.
Highest Common Factor of 1702,7424 is 2
Step 1: Since 7424 > 1702, we apply the division lemma to 7424 and 1702, to get
7424 = 1702 x 4 + 616
Step 2: Since the reminder 1702 ≠ 0, we apply division lemma to 616 and 1702, to get
1702 = 616 x 2 + 470
Step 3: We consider the new divisor 616 and the new remainder 470, and apply the division lemma to get
616 = 470 x 1 + 146
We consider the new divisor 470 and the new remainder 146,and apply the division lemma to get
470 = 146 x 3 + 32
We consider the new divisor 146 and the new remainder 32,and apply the division lemma to get
146 = 32 x 4 + 18
We consider the new divisor 32 and the new remainder 18,and apply the division lemma to get
32 = 18 x 1 + 14
We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get
18 = 14 x 1 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1702 and 7424 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(32,18) = HCF(146,32) = HCF(470,146) = HCF(616,470) = HCF(1702,616) = HCF(7424,1702) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 1702, 7424 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 1702, 7424?
Answer: HCF of 1702, 7424 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1702, 7424 using Euclid's Algorithm?
Answer: For arbitrary numbers 1702, 7424 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.