Highest Common Factor of 360, 574 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 360, 574 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 574 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 360, 574 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 360, 574 is 2.
HCF(360, 574) = 2
HCF of 360, 574 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 360, 574 is 2.
Highest Common Factor of 360,574 is 2
Step 1: Since 574 > 360, we apply the division lemma to 574 and 360, to get
574 = 360 x 1 + 214
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 214 and 360, to get
360 = 214 x 1 + 146
Step 3: We consider the new divisor 214 and the new remainder 146, and apply the division lemma to get
214 = 146 x 1 + 68
We consider the new divisor 146 and the new remainder 68,and apply the division lemma to get
146 = 68 x 2 + 10
We consider the new divisor 68 and the new remainder 10,and apply the division lemma to get
68 = 10 x 6 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
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 360 and 574 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(68,10) = HCF(146,68) = HCF(214,146) = HCF(360,214) = HCF(574,360) .
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Frequently Asked Questions on HCF of 360, 574 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 360, 574?
Answer: HCF of 360, 574 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 574 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 574 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
