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 7660, 3591, 68534 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7660, 3591, 68534 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 7660, 3591, 68534 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 7660, 3591, 68534 is 1.
HCF(7660, 3591, 68534) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7660, 3591, 68534 is 1.
Step 1: Since 7660 > 3591, we apply the division lemma to 7660 and 3591, to get
7660 = 3591 x 2 + 478
Step 2: Since the reminder 3591 ≠ 0, we apply division lemma to 478 and 3591, to get
3591 = 478 x 7 + 245
Step 3: We consider the new divisor 478 and the new remainder 245, and apply the division lemma to get
478 = 245 x 1 + 233
We consider the new divisor 245 and the new remainder 233,and apply the division lemma to get
245 = 233 x 1 + 12
We consider the new divisor 233 and the new remainder 12,and apply the division lemma to get
233 = 12 x 19 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 7660 and 3591 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(233,12) = HCF(245,233) = HCF(478,245) = HCF(3591,478) = HCF(7660,3591) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 68534 > 1, we apply the division lemma to 68534 and 1, to get
68534 = 1 x 68534 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 68534 is 1
Notice that 1 = HCF(68534,1) .
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 7660, 3591, 68534?
Answer: HCF of 7660, 3591, 68534 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7660, 3591, 68534 using Euclid's Algorithm?
Answer: For arbitrary numbers 7660, 3591, 68534 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.