Highest Common Factor of 345, 944, 73 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, 944, 73 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 345, 944, 73 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, 944, 73 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, 944, 73 is 1.
HCF(345, 944, 73) = 1
HCF of 345, 944, 73 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, 944, 73 is 1.
Highest Common Factor of 345,944,73 is 1
Step 1: Since 944 > 345, we apply the division lemma to 944 and 345, to get
944 = 345 x 2 + 254
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 254 and 345, to get
345 = 254 x 1 + 91
Step 3: We consider the new divisor 254 and the new remainder 91, and apply the division lemma to get
254 = 91 x 2 + 72
We consider the new divisor 91 and the new remainder 72,and apply the division lemma to get
91 = 72 x 1 + 19
We consider the new divisor 72 and the new remainder 19,and apply the division lemma to get
72 = 19 x 3 + 15
We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get
19 = 15 x 1 + 4
We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get
15 = 4 x 3 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 345 and 944 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(72,19) = HCF(91,72) = HCF(254,91) = HCF(345,254) = HCF(944,345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 73 > 1, we apply the division lemma to 73 and 1, to get
73 = 1 x 73 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 73 is 1
Notice that 1 = HCF(73,1) .
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Frequently Asked Questions on HCF of 345, 944, 73 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, 944, 73?
Answer: HCF of 345, 944, 73 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 345, 944, 73 using Euclid's Algorithm?
Answer: For arbitrary numbers 345, 944, 73 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
