Highest Common Factor of 902, 55717 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 902, 55717 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 902, 55717 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 902, 55717 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 902, 55717 is 1.
HCF(902, 55717) = 1
HCF of 902, 55717 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 902, 55717 is 1.
Highest Common Factor of 902,55717 is 1
Step 1: Since 55717 > 902, we apply the division lemma to 55717 and 902, to get
55717 = 902 x 61 + 695
Step 2: Since the reminder 902 ≠ 0, we apply division lemma to 695 and 902, to get
902 = 695 x 1 + 207
Step 3: We consider the new divisor 695 and the new remainder 207, and apply the division lemma to get
695 = 207 x 3 + 74
We consider the new divisor 207 and the new remainder 74,and apply the division lemma to get
207 = 74 x 2 + 59
We consider the new divisor 74 and the new remainder 59,and apply the division lemma to get
74 = 59 x 1 + 15
We consider the new divisor 59 and the new remainder 15,and apply the division lemma to get
59 = 15 x 3 + 14
We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get
15 = 14 x 1 + 1
We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 902 and 55717 is 1
Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(59,15) = HCF(74,59) = HCF(207,74) = HCF(695,207) = HCF(902,695) = HCF(55717,902) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 902, 55717 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 902, 55717?
Answer: HCF of 902, 55717 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 902, 55717 using Euclid's Algorithm?
Answer: For arbitrary numbers 902, 55717 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.