Highest Common Factor of 574, 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 574, 908 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 574, 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 574, 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 574, 908 is 2.
HCF(574, 908) = 2
HCF of 574, 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 574, 908 is 2.
Highest Common Factor of 574,908 is 2
Step 1: Since 908 > 574, we apply the division lemma to 908 and 574, to get
908 = 574 x 1 + 334
Step 2: Since the reminder 574 ≠ 0, we apply division lemma to 334 and 574, to get
574 = 334 x 1 + 240
Step 3: We consider the new divisor 334 and the new remainder 240, and apply the division lemma to get
334 = 240 x 1 + 94
We consider the new divisor 240 and the new remainder 94,and apply the division lemma to get
240 = 94 x 2 + 52
We consider the new divisor 94 and the new remainder 52,and apply the division lemma to get
94 = 52 x 1 + 42
We consider the new divisor 52 and the new remainder 42,and apply the division lemma to get
52 = 42 x 1 + 10
We consider the new divisor 42 and the new remainder 10,and apply the division lemma to get
42 = 10 x 4 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 574 and 908 is 2
Notice that 2 = HCF(10,2) = HCF(42,10) = HCF(52,42) = HCF(94,52) = HCF(240,94) = HCF(334,240) = HCF(574,334) = HCF(908,574) .
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Frequently Asked Questions on HCF of 574, 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 574, 908?
Answer: HCF of 574, 908 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 574, 908 using Euclid's Algorithm?
Answer: For arbitrary numbers 574, 908 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.