Highest Common Factor of 448, 6000 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 448, 6000 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 448, 6000 is 16 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 448, 6000 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 448, 6000 is 16.
HCF(448, 6000) = 16
HCF of 448, 6000 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 448, 6000 is 16.
Highest Common Factor of 448,6000 is 16
Step 1: Since 6000 > 448, we apply the division lemma to 6000 and 448, to get
6000 = 448 x 13 + 176
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 176 and 448, to get
448 = 176 x 2 + 96
Step 3: We consider the new divisor 176 and the new remainder 96, and apply the division lemma to get
176 = 96 x 1 + 80
We consider the new divisor 96 and the new remainder 80,and apply the division lemma to get
96 = 80 x 1 + 16
We consider the new divisor 80 and the new remainder 16,and apply the division lemma to get
80 = 16 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 448 and 6000 is 16
Notice that 16 = HCF(80,16) = HCF(96,80) = HCF(176,96) = HCF(448,176) = HCF(6000,448) .
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Frequently Asked Questions on HCF of 448, 6000 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 448, 6000?
Answer: HCF of 448, 6000 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 448, 6000 using Euclid's Algorithm?
Answer: For arbitrary numbers 448, 6000 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.