Highest Common Factor of 493, 850, 45 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 493, 850, 45 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 493, 850, 45 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 493, 850, 45 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 493, 850, 45 is 1.
HCF(493, 850, 45) = 1
HCF of 493, 850, 45 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 493, 850, 45 is 1.
Highest Common Factor of 493,850,45 is 1
Step 1: Since 850 > 493, we apply the division lemma to 850 and 493, to get
850 = 493 x 1 + 357
Step 2: Since the reminder 493 ≠ 0, we apply division lemma to 357 and 493, to get
493 = 357 x 1 + 136
Step 3: We consider the new divisor 357 and the new remainder 136, and apply the division lemma to get
357 = 136 x 2 + 85
We consider the new divisor 136 and the new remainder 85,and apply the division lemma to get
136 = 85 x 1 + 51
We consider the new divisor 85 and the new remainder 51,and apply the division lemma to get
85 = 51 x 1 + 34
We consider the new divisor 51 and the new remainder 34,and apply the division lemma to get
51 = 34 x 1 + 17
We consider the new divisor 34 and the new remainder 17,and apply the division lemma to get
34 = 17 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 493 and 850 is 17
Notice that 17 = HCF(34,17) = HCF(51,34) = HCF(85,51) = HCF(136,85) = HCF(357,136) = HCF(493,357) = HCF(850,493) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45 > 17, we apply the division lemma to 45 and 17, to get
45 = 17 x 2 + 11
Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 11 and 17, to get
17 = 11 x 1 + 6
Step 3: We consider the new divisor 11 and the new remainder 6, and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 17 and 45 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(45,17) .
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Frequently Asked Questions on HCF of 493, 850, 45 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 493, 850, 45?
Answer: HCF of 493, 850, 45 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 493, 850, 45 using Euclid's Algorithm?
Answer: For arbitrary numbers 493, 850, 45 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.