Highest Common Factor of 900, 8444, 4970 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 900, 8444, 4970 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 900, 8444, 4970 is 2 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 900, 8444, 4970 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 900, 8444, 4970 is 2.
HCF(900, 8444, 4970) = 2
HCF of 900, 8444, 4970 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 900, 8444, 4970 is 2.
Highest Common Factor of 900,8444,4970 is 2
Step 1: Since 8444 > 900, we apply the division lemma to 8444 and 900, to get
8444 = 900 x 9 + 344
Step 2: Since the reminder 900 ≠ 0, we apply division lemma to 344 and 900, to get
900 = 344 x 2 + 212
Step 3: We consider the new divisor 344 and the new remainder 212, and apply the division lemma to get
344 = 212 x 1 + 132
We consider the new divisor 212 and the new remainder 132,and apply the division lemma to get
212 = 132 x 1 + 80
We consider the new divisor 132 and the new remainder 80,and apply the division lemma to get
132 = 80 x 1 + 52
We consider the new divisor 80 and the new remainder 52,and apply the division lemma to get
80 = 52 x 1 + 28
We consider the new divisor 52 and the new remainder 28,and apply the division lemma to get
52 = 28 x 1 + 24
We consider the new divisor 28 and the new remainder 24,and apply the division lemma to get
28 = 24 x 1 + 4
We consider the new divisor 24 and the new remainder 4,and apply the division lemma to get
24 = 4 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 900 and 8444 is 4
Notice that 4 = HCF(24,4) = HCF(28,24) = HCF(52,28) = HCF(80,52) = HCF(132,80) = HCF(212,132) = HCF(344,212) = HCF(900,344) = HCF(8444,900) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4970 > 4, we apply the division lemma to 4970 and 4, to get
4970 = 4 x 1242 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 4970 is 2
Notice that 2 = HCF(4,2) = HCF(4970,4) .
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Frequently Asked Questions on HCF of 900, 8444, 4970 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 900, 8444, 4970?
Answer: HCF of 900, 8444, 4970 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 900, 8444, 4970 using Euclid's Algorithm?
Answer: For arbitrary numbers 900, 8444, 4970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
