Highest Common Factor of 409, 667, 253 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 409, 667, 253 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 409, 667, 253 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 409, 667, 253 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 409, 667, 253 is 1.
HCF(409, 667, 253) = 1
HCF of 409, 667, 253 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 409, 667, 253 is 1.
Highest Common Factor of 409,667,253 is 1
Step 1: Since 667 > 409, we apply the division lemma to 667 and 409, to get
667 = 409 x 1 + 258
Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 258 and 409, to get
409 = 258 x 1 + 151
Step 3: We consider the new divisor 258 and the new remainder 151, and apply the division lemma to get
258 = 151 x 1 + 107
We consider the new divisor 151 and the new remainder 107,and apply the division lemma to get
151 = 107 x 1 + 44
We consider the new divisor 107 and the new remainder 44,and apply the division lemma to get
107 = 44 x 2 + 19
We consider the new divisor 44 and the new remainder 19,and apply the division lemma to get
44 = 19 x 2 + 6
We consider the new divisor 19 and the new remainder 6,and apply the division lemma to get
19 = 6 x 3 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 409 and 667 is 1
Notice that 1 = HCF(6,1) = HCF(19,6) = HCF(44,19) = HCF(107,44) = HCF(151,107) = HCF(258,151) = HCF(409,258) = HCF(667,409) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 253 > 1, we apply the division lemma to 253 and 1, to get
253 = 1 x 253 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 253 is 1
Notice that 1 = HCF(253,1) .
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Frequently Asked Questions on HCF of 409, 667, 253 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 409, 667, 253?
Answer: HCF of 409, 667, 253 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 409, 667, 253 using Euclid's Algorithm?
Answer: For arbitrary numbers 409, 667, 253 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.