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 1742, 7665 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1742, 7665 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 1742, 7665 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 1742, 7665 is 1.
HCF(1742, 7665) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1742, 7665 is 1.
Step 1: Since 7665 > 1742, we apply the division lemma to 7665 and 1742, to get
7665 = 1742 x 4 + 697
Step 2: Since the reminder 1742 ≠ 0, we apply division lemma to 697 and 1742, to get
1742 = 697 x 2 + 348
Step 3: We consider the new divisor 697 and the new remainder 348, and apply the division lemma to get
697 = 348 x 2 + 1
We consider the new divisor 348 and the new remainder 1, and apply the division lemma to get
348 = 1 x 348 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1742 and 7665 is 1
Notice that 1 = HCF(348,1) = HCF(697,348) = HCF(1742,697) = HCF(7665,1742) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 1742, 7665?
Answer: HCF of 1742, 7665 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1742, 7665 using Euclid's Algorithm?
Answer: For arbitrary numbers 1742, 7665 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.