Highest Common Factor of 874, 9675, 7608 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 874, 9675, 7608 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 874, 9675, 7608 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 874, 9675, 7608 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 874, 9675, 7608 is 1.
HCF(874, 9675, 7608) = 1
HCF of 874, 9675, 7608 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 874, 9675, 7608 is 1.
Highest Common Factor of 874,9675,7608 is 1
Step 1: Since 9675 > 874, we apply the division lemma to 9675 and 874, to get
9675 = 874 x 11 + 61
Step 2: Since the reminder 874 ≠ 0, we apply division lemma to 61 and 874, to get
874 = 61 x 14 + 20
Step 3: We consider the new divisor 61 and the new remainder 20, and apply the division lemma to get
61 = 20 x 3 + 1
We consider the new divisor 20 and the new remainder 1, and apply the division lemma to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 874 and 9675 is 1
Notice that 1 = HCF(20,1) = HCF(61,20) = HCF(874,61) = HCF(9675,874) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7608 > 1, we apply the division lemma to 7608 and 1, to get
7608 = 1 x 7608 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7608 is 1
Notice that 1 = HCF(7608,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 874, 9675, 7608 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 874, 9675, 7608?
Answer: HCF of 874, 9675, 7608 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 874, 9675, 7608 using Euclid's Algorithm?
Answer: For arbitrary numbers 874, 9675, 7608 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
