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 735, 422, 309 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 735, 422, 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 735, 422, 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 735, 422, 309 is 1.
HCF(735, 422, 309) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 735, 422, 309 is 1.
Step 1: Since 735 > 422, we apply the division lemma to 735 and 422, to get
735 = 422 x 1 + 313
Step 2: Since the reminder 422 ≠ 0, we apply division lemma to 313 and 422, to get
422 = 313 x 1 + 109
Step 3: We consider the new divisor 313 and the new remainder 109, and apply the division lemma to get
313 = 109 x 2 + 95
We consider the new divisor 109 and the new remainder 95,and apply the division lemma to get
109 = 95 x 1 + 14
We consider the new divisor 95 and the new remainder 14,and apply the division lemma to get
95 = 14 x 6 + 11
We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get
14 = 11 x 1 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 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 735 and 422 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(95,14) = HCF(109,95) = HCF(313,109) = HCF(422,313) = HCF(735,422) .
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 735, 422, 309?
Answer: HCF of 735, 422, 309 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 735, 422, 309 using Euclid's Algorithm?
Answer: For arbitrary numbers 735, 422, 309 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.