Highest Common Factor of 2628, 7000 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 2628, 7000 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 2628, 7000 is 4 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 2628, 7000 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 2628, 7000 is 4.
HCF(2628, 7000) = 4
HCF of 2628, 7000 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2628, 7000 is 4.
Highest Common Factor of 2628,7000 is 4
Step 1: Since 7000 > 2628, we apply the division lemma to 7000 and 2628, to get
7000 = 2628 x 2 + 1744
Step 2: Since the reminder 2628 ≠ 0, we apply division lemma to 1744 and 2628, to get
2628 = 1744 x 1 + 884
Step 3: We consider the new divisor 1744 and the new remainder 884, and apply the division lemma to get
1744 = 884 x 1 + 860
We consider the new divisor 884 and the new remainder 860,and apply the division lemma to get
884 = 860 x 1 + 24
We consider the new divisor 860 and the new remainder 24,and apply the division lemma to get
860 = 24 x 35 + 20
We consider the new divisor 24 and the new remainder 20,and apply the division lemma to get
24 = 20 x 1 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 2628 and 7000 is 4
Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(860,24) = HCF(884,860) = HCF(1744,884) = HCF(2628,1744) = HCF(7000,2628) .
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Frequently Asked Questions on HCF of 2628, 7000 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 2628, 7000?
Answer: HCF of 2628, 7000 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2628, 7000 using Euclid's Algorithm?
Answer: For arbitrary numbers 2628, 7000 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.