Highest Common Factor of 905, 415, 102, 762 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, 415, 102, 762 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 905, 415, 102, 762 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, 415, 102, 762 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, 415, 102, 762 is 1.
HCF(905, 415, 102, 762) = 1
HCF of 905, 415, 102, 762 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, 415, 102, 762 is 1.
Highest Common Factor of 905,415,102,762 is 1
Step 1: Since 905 > 415, we apply the division lemma to 905 and 415, to get
905 = 415 x 2 + 75
Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 75 and 415, to get
415 = 75 x 5 + 40
Step 3: We consider the new divisor 75 and the new remainder 40, and apply the division lemma to get
75 = 40 x 1 + 35
We consider the new divisor 40 and the new remainder 35,and apply the division lemma to get
40 = 35 x 1 + 5
We consider the new divisor 35 and the new remainder 5,and apply the division lemma to get
35 = 5 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 905 and 415 is 5
Notice that 5 = HCF(35,5) = HCF(40,35) = HCF(75,40) = HCF(415,75) = HCF(905,415) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 102 > 5, we apply the division lemma to 102 and 5, to get
102 = 5 x 20 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: 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 5 and 102 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(102,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 762 > 1, we apply the division lemma to 762 and 1, to get
762 = 1 x 762 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 762 is 1
Notice that 1 = HCF(762,1) .
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Frequently Asked Questions on HCF of 905, 415, 102, 762 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, 415, 102, 762?
Answer: HCF of 905, 415, 102, 762 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 905, 415, 102, 762 using Euclid's Algorithm?
Answer: For arbitrary numbers 905, 415, 102, 762 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.