Highest Common Factor of 705, 748, 706 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, 748, 706 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 748, 706 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, 748, 706 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, 748, 706 is 1.
HCF(705, 748, 706) = 1
HCF of 705, 748, 706 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, 748, 706 is 1.
Highest Common Factor of 705,748,706 is 1
Step 1: Since 748 > 705, we apply the division lemma to 748 and 705, to get
748 = 705 x 1 + 43
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 43 and 705, to get
705 = 43 x 16 + 17
Step 3: We consider the new divisor 43 and the new remainder 17, and apply the division lemma to get
43 = 17 x 2 + 9
We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get
17 = 9 x 1 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 705 and 748 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(43,17) = HCF(705,43) = HCF(748,705) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 706 > 1, we apply the division lemma to 706 and 1, to get
706 = 1 x 706 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 706 is 1
Notice that 1 = HCF(706,1) .
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Frequently Asked Questions on HCF of 705, 748, 706 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, 748, 706?
Answer: HCF of 705, 748, 706 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 748, 706 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 748, 706 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.