Highest Common Factor of 495, 310, 93 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 495, 310, 93 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 495, 310, 93 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 495, 310, 93 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 495, 310, 93 is 1.
HCF(495, 310, 93) = 1
HCF of 495, 310, 93 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 495, 310, 93 is 1.
Highest Common Factor of 495,310,93 is 1
Step 1: Since 495 > 310, we apply the division lemma to 495 and 310, to get
495 = 310 x 1 + 185
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 185 and 310, to get
310 = 185 x 1 + 125
Step 3: We consider the new divisor 185 and the new remainder 125, and apply the division lemma to get
185 = 125 x 1 + 60
We consider the new divisor 125 and the new remainder 60,and apply the division lemma to get
125 = 60 x 2 + 5
We consider the new divisor 60 and the new remainder 5,and apply the division lemma to get
60 = 5 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 495 and 310 is 5
Notice that 5 = HCF(60,5) = HCF(125,60) = HCF(185,125) = HCF(310,185) = HCF(495,310) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 93 > 5, we apply the division lemma to 93 and 5, to get
93 = 5 x 18 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: 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 5 and 93 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(93,5) .
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Frequently Asked Questions on HCF of 495, 310, 93 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 495, 310, 93?
Answer: HCF of 495, 310, 93 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 495, 310, 93 using Euclid's Algorithm?
Answer: For arbitrary numbers 495, 310, 93 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.