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 545, 943, 309 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 545, 943, 309 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 545, 943, 309 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 545, 943, 309 is 1.
HCF(545, 943, 309) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 545, 943, 309 is 1.
Step 1: Since 943 > 545, we apply the division lemma to 943 and 545, to get
943 = 545 x 1 + 398
Step 2: Since the reminder 545 ≠ 0, we apply division lemma to 398 and 545, to get
545 = 398 x 1 + 147
Step 3: We consider the new divisor 398 and the new remainder 147, and apply the division lemma to get
398 = 147 x 2 + 104
We consider the new divisor 147 and the new remainder 104,and apply the division lemma to get
147 = 104 x 1 + 43
We consider the new divisor 104 and the new remainder 43,and apply the division lemma to get
104 = 43 x 2 + 18
We consider the new divisor 43 and the new remainder 18,and apply the division lemma to get
43 = 18 x 2 + 7
We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get
18 = 7 x 2 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 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 545 and 943 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(43,18) = HCF(104,43) = HCF(147,104) = HCF(398,147) = HCF(545,398) = HCF(943,545) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 309 > 1, we apply the division lemma to 309 and 1, to get
309 = 1 x 309 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 309 is 1
Notice that 1 = HCF(309,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 545, 943, 309?
Answer: HCF of 545, 943, 309 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 545, 943, 309 using Euclid's Algorithm?
Answer: For arbitrary numbers 545, 943, 309 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.