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 2345, 7697, 97004 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2345, 7697, 97004 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 2345, 7697, 97004 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 2345, 7697, 97004 is 1.
HCF(2345, 7697, 97004) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2345, 7697, 97004 is 1.
Step 1: Since 7697 > 2345, we apply the division lemma to 7697 and 2345, to get
7697 = 2345 x 3 + 662
Step 2: Since the reminder 2345 ≠ 0, we apply division lemma to 662 and 2345, to get
2345 = 662 x 3 + 359
Step 3: We consider the new divisor 662 and the new remainder 359, and apply the division lemma to get
662 = 359 x 1 + 303
We consider the new divisor 359 and the new remainder 303,and apply the division lemma to get
359 = 303 x 1 + 56
We consider the new divisor 303 and the new remainder 56,and apply the division lemma to get
303 = 56 x 5 + 23
We consider the new divisor 56 and the new remainder 23,and apply the division lemma to get
56 = 23 x 2 + 10
We consider the new divisor 23 and the new remainder 10,and apply the division lemma to get
23 = 10 x 2 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2345 and 7697 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(23,10) = HCF(56,23) = HCF(303,56) = HCF(359,303) = HCF(662,359) = HCF(2345,662) = HCF(7697,2345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 97004 > 1, we apply the division lemma to 97004 and 1, to get
97004 = 1 x 97004 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 97004 is 1
Notice that 1 = HCF(97004,1) .
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 2345, 7697, 97004?
Answer: HCF of 2345, 7697, 97004 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2345, 7697, 97004 using Euclid's Algorithm?
Answer: For arbitrary numbers 2345, 7697, 97004 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.