Highest Common Factor of 558, 900, 908 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 558, 900, 908 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 558, 900, 908 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 558, 900, 908 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 558, 900, 908 is 2.
HCF(558, 900, 908) = 2
HCF of 558, 900, 908 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 558, 900, 908 is 2.
Highest Common Factor of 558,900,908 is 2
Step 1: Since 900 > 558, we apply the division lemma to 900 and 558, to get
900 = 558 x 1 + 342
Step 2: Since the reminder 558 ≠ 0, we apply division lemma to 342 and 558, to get
558 = 342 x 1 + 216
Step 3: We consider the new divisor 342 and the new remainder 216, and apply the division lemma to get
342 = 216 x 1 + 126
We consider the new divisor 216 and the new remainder 126,and apply the division lemma to get
216 = 126 x 1 + 90
We consider the new divisor 126 and the new remainder 90,and apply the division lemma to get
126 = 90 x 1 + 36
We consider the new divisor 90 and the new remainder 36,and apply the division lemma to get
90 = 36 x 2 + 18
We consider the new divisor 36 and the new remainder 18,and apply the division lemma to get
36 = 18 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 558 and 900 is 18
Notice that 18 = HCF(36,18) = HCF(90,36) = HCF(126,90) = HCF(216,126) = HCF(342,216) = HCF(558,342) = HCF(900,558) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 908 > 18, we apply the division lemma to 908 and 18, to get
908 = 18 x 50 + 8
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 8 and 18, to get
18 = 8 x 2 + 2
Step 3: We consider the new divisor 8 and the new remainder 2, and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 18 and 908 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(908,18) .
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Frequently Asked Questions on HCF of 558, 900, 908 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 558, 900, 908?
Answer: HCF of 558, 900, 908 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 558, 900, 908 using Euclid's Algorithm?
Answer: For arbitrary numbers 558, 900, 908 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.