Highest Common Factor of 908, 498, 137 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 908, 498, 137 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 908, 498, 137 is 1 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 908, 498, 137 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 908, 498, 137 is 1.
HCF(908, 498, 137) = 1
HCF of 908, 498, 137 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 908, 498, 137 is 1.
Highest Common Factor of 908,498,137 is 1
Step 1: Since 908 > 498, we apply the division lemma to 908 and 498, to get
908 = 498 x 1 + 410
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 410 and 498, to get
498 = 410 x 1 + 88
Step 3: We consider the new divisor 410 and the new remainder 88, and apply the division lemma to get
410 = 88 x 4 + 58
We consider the new divisor 88 and the new remainder 58,and apply the division lemma to get
88 = 58 x 1 + 30
We consider the new divisor 58 and the new remainder 30,and apply the division lemma to get
58 = 30 x 1 + 28
We consider the new divisor 30 and the new remainder 28,and apply the division lemma to get
30 = 28 x 1 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 908 and 498 is 2
Notice that 2 = HCF(28,2) = HCF(30,28) = HCF(58,30) = HCF(88,58) = HCF(410,88) = HCF(498,410) = HCF(908,498) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 137 > 2, we apply the division lemma to 137 and 2, to get
137 = 2 x 68 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 137 is 1
Notice that 1 = HCF(2,1) = HCF(137,2) .
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Frequently Asked Questions on HCF of 908, 498, 137 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 908, 498, 137?
Answer: HCF of 908, 498, 137 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 908, 498, 137 using Euclid's Algorithm?
Answer: For arbitrary numbers 908, 498, 137 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.