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 8983, 5037, 64513 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8983, 5037, 64513 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 8983, 5037, 64513 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 8983, 5037, 64513 is 1.
HCF(8983, 5037, 64513) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8983, 5037, 64513 is 1.
Step 1: Since 8983 > 5037, we apply the division lemma to 8983 and 5037, to get
8983 = 5037 x 1 + 3946
Step 2: Since the reminder 5037 ≠ 0, we apply division lemma to 3946 and 5037, to get
5037 = 3946 x 1 + 1091
Step 3: We consider the new divisor 3946 and the new remainder 1091, and apply the division lemma to get
3946 = 1091 x 3 + 673
We consider the new divisor 1091 and the new remainder 673,and apply the division lemma to get
1091 = 673 x 1 + 418
We consider the new divisor 673 and the new remainder 418,and apply the division lemma to get
673 = 418 x 1 + 255
We consider the new divisor 418 and the new remainder 255,and apply the division lemma to get
418 = 255 x 1 + 163
We consider the new divisor 255 and the new remainder 163,and apply the division lemma to get
255 = 163 x 1 + 92
We consider the new divisor 163 and the new remainder 92,and apply the division lemma to get
163 = 92 x 1 + 71
We consider the new divisor 92 and the new remainder 71,and apply the division lemma to get
92 = 71 x 1 + 21
We consider the new divisor 71 and the new remainder 21,and apply the division lemma to get
71 = 21 x 3 + 8
We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get
21 = 8 x 2 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 8983 and 5037 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(71,21) = HCF(92,71) = HCF(163,92) = HCF(255,163) = HCF(418,255) = HCF(673,418) = HCF(1091,673) = HCF(3946,1091) = HCF(5037,3946) = HCF(8983,5037) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 64513 > 1, we apply the division lemma to 64513 and 1, to get
64513 = 1 x 64513 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 64513 is 1
Notice that 1 = HCF(64513,1) .
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 8983, 5037, 64513?
Answer: HCF of 8983, 5037, 64513 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8983, 5037, 64513 using Euclid's Algorithm?
Answer: For arbitrary numbers 8983, 5037, 64513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.