Highest Common Factor of 905, 6989 using Euclid's algorithm
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 905, 6989 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 905, 6989 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 905, 6989 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 905, 6989 is 1.
HCF(905, 6989) = 1
HCF of 905, 6989 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 905, 6989 is 1.
Highest Common Factor of 905,6989 is 1
Step 1: Since 6989 > 905, we apply the division lemma to 6989 and 905, to get
6989 = 905 x 7 + 654
Step 2: Since the reminder 905 ≠ 0, we apply division lemma to 654 and 905, to get
905 = 654 x 1 + 251
Step 3: We consider the new divisor 654 and the new remainder 251, and apply the division lemma to get
654 = 251 x 2 + 152
We consider the new divisor 251 and the new remainder 152,and apply the division lemma to get
251 = 152 x 1 + 99
We consider the new divisor 152 and the new remainder 99,and apply the division lemma to get
152 = 99 x 1 + 53
We consider the new divisor 99 and the new remainder 53,and apply the division lemma to get
99 = 53 x 1 + 46
We consider the new divisor 53 and the new remainder 46,and apply the division lemma to get
53 = 46 x 1 + 7
We consider the new divisor 46 and the new remainder 7,and apply the division lemma to get
46 = 7 x 6 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 905 and 6989 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(46,7) = HCF(53,46) = HCF(99,53) = HCF(152,99) = HCF(251,152) = HCF(654,251) = HCF(905,654) = HCF(6989,905) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 905, 6989 using Euclid's Algorithm
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 905, 6989?
Answer: HCF of 905, 6989 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 905, 6989 using Euclid's Algorithm?
Answer: For arbitrary numbers 905, 6989 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.