Highest Common Factor of 305, 492 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 305, 492 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 305, 492 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 305, 492 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 305, 492 is 1.
HCF(305, 492) = 1
HCF of 305, 492 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 305, 492 is 1.
Highest Common Factor of 305,492 is 1
Step 1: Since 492 > 305, we apply the division lemma to 492 and 305, to get
492 = 305 x 1 + 187
Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 187 and 305, to get
305 = 187 x 1 + 118
Step 3: We consider the new divisor 187 and the new remainder 118, and apply the division lemma to get
187 = 118 x 1 + 69
We consider the new divisor 118 and the new remainder 69,and apply the division lemma to get
118 = 69 x 1 + 49
We consider the new divisor 69 and the new remainder 49,and apply the division lemma to get
69 = 49 x 1 + 20
We consider the new divisor 49 and the new remainder 20,and apply the division lemma to get
49 = 20 x 2 + 9
We consider the new divisor 20 and the new remainder 9,and apply the division lemma to get
20 = 9 x 2 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 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 305 and 492 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(49,20) = HCF(69,49) = HCF(118,69) = HCF(187,118) = HCF(305,187) = HCF(492,305) .
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Frequently Asked Questions on HCF of 305, 492 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 305, 492?
Answer: HCF of 305, 492 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 305, 492 using Euclid's Algorithm?
Answer: For arbitrary numbers 305, 492 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
