Highest Common Factor of 905, 802 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, 802 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 905, 802 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, 802 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, 802 is 1.
HCF(905, 802) = 1
HCF of 905, 802 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, 802 is 1.
Highest Common Factor of 905,802 is 1
Step 1: Since 905 > 802, we apply the division lemma to 905 and 802, to get
905 = 802 x 1 + 103
Step 2: Since the reminder 802 ≠ 0, we apply division lemma to 103 and 802, to get
802 = 103 x 7 + 81
Step 3: We consider the new divisor 103 and the new remainder 81, and apply the division lemma to get
103 = 81 x 1 + 22
We consider the new divisor 81 and the new remainder 22,and apply the division lemma to get
81 = 22 x 3 + 15
We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get
22 = 15 x 1 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 905 and 802 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(81,22) = HCF(103,81) = HCF(802,103) = HCF(905,802) .
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Frequently Asked Questions on HCF of 905, 802 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, 802?
Answer: HCF of 905, 802 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 905, 802 using Euclid's Algorithm?
Answer: For arbitrary numbers 905, 802 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.