Highest Common Factor of 2000, 1408 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 2000, 1408 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 2000, 1408 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 2000, 1408 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 2000, 1408 is 16.
HCF(2000, 1408) = 16
HCF of 2000, 1408 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2000, 1408 is 16.
Highest Common Factor of 2000,1408 is 16
Step 1: Since 2000 > 1408, we apply the division lemma to 2000 and 1408, to get
2000 = 1408 x 1 + 592
Step 2: Since the reminder 1408 ≠ 0, we apply division lemma to 592 and 1408, to get
1408 = 592 x 2 + 224
Step 3: We consider the new divisor 592 and the new remainder 224, and apply the division lemma to get
592 = 224 x 2 + 144
We consider the new divisor 224 and the new remainder 144,and apply the division lemma to get
224 = 144 x 1 + 80
We consider the new divisor 144 and the new remainder 80,and apply the division lemma to get
144 = 80 x 1 + 64
We consider the new divisor 80 and the new remainder 64,and apply the division lemma to get
80 = 64 x 1 + 16
We consider the new divisor 64 and the new remainder 16,and apply the division lemma to get
64 = 16 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 2000 and 1408 is 16
Notice that 16 = HCF(64,16) = HCF(80,64) = HCF(144,80) = HCF(224,144) = HCF(592,224) = HCF(1408,592) = HCF(2000,1408) .
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Frequently Asked Questions on HCF of 2000, 1408 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 2000, 1408?
Answer: HCF of 2000, 1408 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2000, 1408 using Euclid's Algorithm?
Answer: For arbitrary numbers 2000, 1408 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.