Highest Common Factor of 662, 905, 101 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 662, 905, 101 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 662, 905, 101 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 662, 905, 101 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 662, 905, 101 is 1.
HCF(662, 905, 101) = 1
HCF of 662, 905, 101 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 662, 905, 101 is 1.
Highest Common Factor of 662,905,101 is 1
Step 1: Since 905 > 662, we apply the division lemma to 905 and 662, to get
905 = 662 x 1 + 243
Step 2: Since the reminder 662 ≠ 0, we apply division lemma to 243 and 662, to get
662 = 243 x 2 + 176
Step 3: We consider the new divisor 243 and the new remainder 176, and apply the division lemma to get
243 = 176 x 1 + 67
We consider the new divisor 176 and the new remainder 67,and apply the division lemma to get
176 = 67 x 2 + 42
We consider the new divisor 67 and the new remainder 42,and apply the division lemma to get
67 = 42 x 1 + 25
We consider the new divisor 42 and the new remainder 25,and apply the division lemma to get
42 = 25 x 1 + 17
We consider the new divisor 25 and the new remainder 17,and apply the division lemma to get
25 = 17 x 1 + 8
We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get
17 = 8 x 2 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 662 and 905 is 1
Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(25,17) = HCF(42,25) = HCF(67,42) = HCF(176,67) = HCF(243,176) = HCF(662,243) = HCF(905,662) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 101 > 1, we apply the division lemma to 101 and 1, to get
101 = 1 x 101 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 101 is 1
Notice that 1 = HCF(101,1) .
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Frequently Asked Questions on HCF of 662, 905, 101 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 662, 905, 101?
Answer: HCF of 662, 905, 101 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 662, 905, 101 using Euclid's Algorithm?
Answer: For arbitrary numbers 662, 905, 101 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.