Highest Common Factor of 345, 903, 653, 266 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 345, 903, 653, 266 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 345, 903, 653, 266 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 345, 903, 653, 266 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 345, 903, 653, 266 is 1.
HCF(345, 903, 653, 266) = 1
HCF of 345, 903, 653, 266 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 345, 903, 653, 266 is 1.
Highest Common Factor of 345,903,653,266 is 1
Step 1: Since 903 > 345, we apply the division lemma to 903 and 345, to get
903 = 345 x 2 + 213
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 213 and 345, to get
345 = 213 x 1 + 132
Step 3: We consider the new divisor 213 and the new remainder 132, and apply the division lemma to get
213 = 132 x 1 + 81
We consider the new divisor 132 and the new remainder 81,and apply the division lemma to get
132 = 81 x 1 + 51
We consider the new divisor 81 and the new remainder 51,and apply the division lemma to get
81 = 51 x 1 + 30
We consider the new divisor 51 and the new remainder 30,and apply the division lemma to get
51 = 30 x 1 + 21
We consider the new divisor 30 and the new remainder 21,and apply the division lemma to get
30 = 21 x 1 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 345 and 903 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(30,21) = HCF(51,30) = HCF(81,51) = HCF(132,81) = HCF(213,132) = HCF(345,213) = HCF(903,345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 653 > 3, we apply the division lemma to 653 and 3, to get
653 = 3 x 217 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 653 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(653,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 266 > 1, we apply the division lemma to 266 and 1, to get
266 = 1 x 266 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 266 is 1
Notice that 1 = HCF(266,1) .
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Frequently Asked Questions on HCF of 345, 903, 653, 266 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 345, 903, 653, 266?
Answer: HCF of 345, 903, 653, 266 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 345, 903, 653, 266 using Euclid's Algorithm?
Answer: For arbitrary numbers 345, 903, 653, 266 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.