Highest Common Factor of 704, 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 704, 448 i.e. 64 the largest integer that leaves a remainder zero for all numbers.
HCF of 704, 448 is 64 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 704, 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 704, 448 is 64.
HCF(704, 448) = 64
HCF of 704, 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 704, 448 is 64.
Highest Common Factor of 704,448 is 64
Step 1: Since 704 > 448, we apply the division lemma to 704 and 448, to get
704 = 448 x 1 + 256
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 256 and 448, to get
448 = 256 x 1 + 192
Step 3: We consider the new divisor 256 and the new remainder 192, and apply the division lemma to get
256 = 192 x 1 + 64
We consider the new divisor 192 and the new remainder 64, and apply the division lemma to get
192 = 64 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 64, the HCF of 704 and 448 is 64
Notice that 64 = HCF(192,64) = HCF(256,192) = HCF(448,256) = HCF(704,448) .
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Frequently Asked Questions on HCF of 704, 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 704, 448?
Answer: HCF of 704, 448 is 64 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 704, 448 using Euclid's Algorithm?
Answer: For arbitrary numbers 704, 448 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.