Highest Common Factor of 407, 925, 82 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 407, 925, 82 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 407, 925, 82 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 407, 925, 82 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 407, 925, 82 is 1.
HCF(407, 925, 82) = 1
HCF of 407, 925, 82 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 407, 925, 82 is 1.
Highest Common Factor of 407,925,82 is 1
Step 1: Since 925 > 407, we apply the division lemma to 925 and 407, to get
925 = 407 x 2 + 111
Step 2: Since the reminder 407 ≠ 0, we apply division lemma to 111 and 407, to get
407 = 111 x 3 + 74
Step 3: We consider the new divisor 111 and the new remainder 74, and apply the division lemma to get
111 = 74 x 1 + 37
We consider the new divisor 74 and the new remainder 37, and apply the division lemma to get
74 = 37 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 37, the HCF of 407 and 925 is 37
Notice that 37 = HCF(74,37) = HCF(111,74) = HCF(407,111) = HCF(925,407) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 82 > 37, we apply the division lemma to 82 and 37, to get
82 = 37 x 2 + 8
Step 2: Since the reminder 37 ≠ 0, we apply division lemma to 8 and 37, to get
37 = 8 x 4 + 5
Step 3: We consider the new divisor 8 and the new remainder 5, and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
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 37 and 82 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(37,8) = HCF(82,37) .
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Frequently Asked Questions on HCF of 407, 925, 82 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 407, 925, 82?
Answer: HCF of 407, 925, 82 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 407, 925, 82 using Euclid's Algorithm?
Answer: For arbitrary numbers 407, 925, 82 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.