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 8024, 2790, 35335 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8024, 2790, 35335 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 8024, 2790, 35335 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 8024, 2790, 35335 is 1.
HCF(8024, 2790, 35335) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8024, 2790, 35335 is 1.
Step 1: Since 8024 > 2790, we apply the division lemma to 8024 and 2790, to get
8024 = 2790 x 2 + 2444
Step 2: Since the reminder 2790 ≠ 0, we apply division lemma to 2444 and 2790, to get
2790 = 2444 x 1 + 346
Step 3: We consider the new divisor 2444 and the new remainder 346, and apply the division lemma to get
2444 = 346 x 7 + 22
We consider the new divisor 346 and the new remainder 22,and apply the division lemma to get
346 = 22 x 15 + 16
We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get
22 = 16 x 1 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 8024 and 2790 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(346,22) = HCF(2444,346) = HCF(2790,2444) = HCF(8024,2790) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 35335 > 2, we apply the division lemma to 35335 and 2, to get
35335 = 2 x 17667 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 35335 is 1
Notice that 1 = HCF(2,1) = HCF(35335,2) .
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 8024, 2790, 35335?
Answer: HCF of 8024, 2790, 35335 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8024, 2790, 35335 using Euclid's Algorithm?
Answer: For arbitrary numbers 8024, 2790, 35335 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.