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, 329, 738 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 329, 738 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, 329, 738 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, 329, 738 is 1.
HCF(705, 329, 738) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 705, 329, 738 is 1.
Step 1: Since 705 > 329, we apply the division lemma to 705 and 329, to get
705 = 329 x 2 + 47
Step 2: Since the reminder 329 ≠ 0, we apply division lemma to 47 and 329, to get
329 = 47 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 47, the HCF of 705 and 329 is 47
Notice that 47 = HCF(329,47) = HCF(705,329) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 738 > 47, we apply the division lemma to 738 and 47, to get
738 = 47 x 15 + 33
Step 2: Since the reminder 47 ≠ 0, we apply division lemma to 33 and 47, to get
47 = 33 x 1 + 14
Step 3: We consider the new divisor 33 and the new remainder 14, and apply the division lemma to get
33 = 14 x 2 + 5
We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get
14 = 5 x 2 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 47 and 738 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(33,14) = HCF(47,33) = HCF(738,47) .
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 705, 329, 738?
Answer: HCF of 705, 329, 738 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 329, 738 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 329, 738 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.