Highest Common Factor of 705, 447, 322 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 705, 447, 322 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 447, 322 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 705, 447, 322 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 705, 447, 322 is 1.
HCF(705, 447, 322) = 1
HCF of 705, 447, 322 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 705, 447, 322 is 1.
Highest Common Factor of 705,447,322 is 1
Step 1: Since 705 > 447, we apply the division lemma to 705 and 447, to get
705 = 447 x 1 + 258
Step 2: Since the reminder 447 ≠ 0, we apply division lemma to 258 and 447, to get
447 = 258 x 1 + 189
Step 3: We consider the new divisor 258 and the new remainder 189, and apply the division lemma to get
258 = 189 x 1 + 69
We consider the new divisor 189 and the new remainder 69,and apply the division lemma to get
189 = 69 x 2 + 51
We consider the new divisor 69 and the new remainder 51,and apply the division lemma to get
69 = 51 x 1 + 18
We consider the new divisor 51 and the new remainder 18,and apply the division lemma to get
51 = 18 x 2 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 705 and 447 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(51,18) = HCF(69,51) = HCF(189,69) = HCF(258,189) = HCF(447,258) = HCF(705,447) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 322 > 3, we apply the division lemma to 322 and 3, to get
322 = 3 x 107 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 322 is 1
Notice that 1 = HCF(3,1) = HCF(322,3) .
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Frequently Asked Questions on HCF of 705, 447, 322 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 705, 447, 322?
Answer: HCF of 705, 447, 322 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 447, 322 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 447, 322 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.