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 7829, 5461, 64728 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7829, 5461, 64728 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 7829, 5461, 64728 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 7829, 5461, 64728 is 1.
HCF(7829, 5461, 64728) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7829, 5461, 64728 is 1.
Step 1: Since 7829 > 5461, we apply the division lemma to 7829 and 5461, to get
7829 = 5461 x 1 + 2368
Step 2: Since the reminder 5461 ≠ 0, we apply division lemma to 2368 and 5461, to get
5461 = 2368 x 2 + 725
Step 3: We consider the new divisor 2368 and the new remainder 725, and apply the division lemma to get
2368 = 725 x 3 + 193
We consider the new divisor 725 and the new remainder 193,and apply the division lemma to get
725 = 193 x 3 + 146
We consider the new divisor 193 and the new remainder 146,and apply the division lemma to get
193 = 146 x 1 + 47
We consider the new divisor 146 and the new remainder 47,and apply the division lemma to get
146 = 47 x 3 + 5
We consider the new divisor 47 and the new remainder 5,and apply the division lemma to get
47 = 5 x 9 + 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 7829 and 5461 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(47,5) = HCF(146,47) = HCF(193,146) = HCF(725,193) = HCF(2368,725) = HCF(5461,2368) = HCF(7829,5461) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 64728 > 1, we apply the division lemma to 64728 and 1, to get
64728 = 1 x 64728 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 64728 is 1
Notice that 1 = HCF(64728,1) .
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 7829, 5461, 64728?
Answer: HCF of 7829, 5461, 64728 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7829, 5461, 64728 using Euclid's Algorithm?
Answer: For arbitrary numbers 7829, 5461, 64728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.