Highest Common Factor of 712, 448 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 712, 448 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 712, 448 is 8 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 712, 448 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 712, 448 is 8.
HCF(712, 448) = 8
HCF of 712, 448 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 712, 448 is 8.
Highest Common Factor of 712,448 is 8
Step 1: Since 712 > 448, we apply the division lemma to 712 and 448, to get
712 = 448 x 1 + 264
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 264 and 448, to get
448 = 264 x 1 + 184
Step 3: We consider the new divisor 264 and the new remainder 184, and apply the division lemma to get
264 = 184 x 1 + 80
We consider the new divisor 184 and the new remainder 80,and apply the division lemma to get
184 = 80 x 2 + 24
We consider the new divisor 80 and the new remainder 24,and apply the division lemma to get
80 = 24 x 3 + 8
We consider the new divisor 24 and the new remainder 8,and apply the division lemma to get
24 = 8 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 712 and 448 is 8
Notice that 8 = HCF(24,8) = HCF(80,24) = HCF(184,80) = HCF(264,184) = HCF(448,264) = HCF(712,448) .
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Frequently Asked Questions on HCF of 712, 448 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 712, 448?
Answer: HCF of 712, 448 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 712, 448 using Euclid's Algorithm?
Answer: For arbitrary numbers 712, 448 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.