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 785, 497, 73 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 785, 497, 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 785, 497, 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 785, 497, 73 is 1.
HCF(785, 497, 73) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 785, 497, 73 is 1.
Step 1: Since 785 > 497, we apply the division lemma to 785 and 497, to get
785 = 497 x 1 + 288
Step 2: Since the reminder 497 ≠ 0, we apply division lemma to 288 and 497, to get
497 = 288 x 1 + 209
Step 3: We consider the new divisor 288 and the new remainder 209, and apply the division lemma to get
288 = 209 x 1 + 79
We consider the new divisor 209 and the new remainder 79,and apply the division lemma to get
209 = 79 x 2 + 51
We consider the new divisor 79 and the new remainder 51,and apply the division lemma to get
79 = 51 x 1 + 28
We consider the new divisor 51 and the new remainder 28,and apply the division lemma to get
51 = 28 x 1 + 23
We consider the new divisor 28 and the new remainder 23,and apply the division lemma to get
28 = 23 x 1 + 5
We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get
23 = 5 x 4 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
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 785 and 497 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(28,23) = HCF(51,28) = HCF(79,51) = HCF(209,79) = HCF(288,209) = HCF(497,288) = HCF(785,497) .
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) .
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 785, 497, 73?
Answer: HCF of 785, 497, 73 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 785, 497, 73 using Euclid's Algorithm?
Answer: For arbitrary numbers 785, 497, 73 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.