Highest Common Factor of 707, 448, 728 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 707, 448, 728 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 707, 448, 728 is 7 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 707, 448, 728 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 707, 448, 728 is 7.
HCF(707, 448, 728) = 7
HCF of 707, 448, 728 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 707, 448, 728 is 7.
Highest Common Factor of 707,448,728 is 7
Step 1: Since 707 > 448, we apply the division lemma to 707 and 448, to get
707 = 448 x 1 + 259
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 259 and 448, to get
448 = 259 x 1 + 189
Step 3: We consider the new divisor 259 and the new remainder 189, and apply the division lemma to get
259 = 189 x 1 + 70
We consider the new divisor 189 and the new remainder 70,and apply the division lemma to get
189 = 70 x 2 + 49
We consider the new divisor 70 and the new remainder 49,and apply the division lemma to get
70 = 49 x 1 + 21
We consider the new divisor 49 and the new remainder 21,and apply the division lemma to get
49 = 21 x 2 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 707 and 448 is 7
Notice that 7 = HCF(21,7) = HCF(49,21) = HCF(70,49) = HCF(189,70) = HCF(259,189) = HCF(448,259) = HCF(707,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 728 > 7, we apply the division lemma to 728 and 7, to get
728 = 7 x 104 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7 and 728 is 7
Notice that 7 = HCF(728,7) .
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Frequently Asked Questions on HCF of 707, 448, 728 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 707, 448, 728?
Answer: HCF of 707, 448, 728 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 707, 448, 728 using Euclid's Algorithm?
Answer: For arbitrary numbers 707, 448, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
