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 6765, 8366, 97388 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6765, 8366, 97388 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 6765, 8366, 97388 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 6765, 8366, 97388 is 1.
HCF(6765, 8366, 97388) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6765, 8366, 97388 is 1.
Step 1: Since 8366 > 6765, we apply the division lemma to 8366 and 6765, to get
8366 = 6765 x 1 + 1601
Step 2: Since the reminder 6765 ≠ 0, we apply division lemma to 1601 and 6765, to get
6765 = 1601 x 4 + 361
Step 3: We consider the new divisor 1601 and the new remainder 361, and apply the division lemma to get
1601 = 361 x 4 + 157
We consider the new divisor 361 and the new remainder 157,and apply the division lemma to get
361 = 157 x 2 + 47
We consider the new divisor 157 and the new remainder 47,and apply the division lemma to get
157 = 47 x 3 + 16
We consider the new divisor 47 and the new remainder 16,and apply the division lemma to get
47 = 16 x 2 + 15
We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get
16 = 15 x 1 + 1
We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6765 and 8366 is 1
Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(47,16) = HCF(157,47) = HCF(361,157) = HCF(1601,361) = HCF(6765,1601) = HCF(8366,6765) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 97388 > 1, we apply the division lemma to 97388 and 1, to get
97388 = 1 x 97388 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 97388 is 1
Notice that 1 = HCF(97388,1) .
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 6765, 8366, 97388?
Answer: HCF of 6765, 8366, 97388 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6765, 8366, 97388 using Euclid's Algorithm?
Answer: For arbitrary numbers 6765, 8366, 97388 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.