Highest Common Factor of 574, 1407 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, 1407 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 574, 1407 is 7 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, 1407 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, 1407 is 7.
HCF(574, 1407) = 7
HCF of 574, 1407 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, 1407 is 7.
Highest Common Factor of 574,1407 is 7
Step 1: Since 1407 > 574, we apply the division lemma to 1407 and 574, to get
1407 = 574 x 2 + 259
Step 2: Since the reminder 574 ≠ 0, we apply division lemma to 259 and 574, to get
574 = 259 x 2 + 56
Step 3: We consider the new divisor 259 and the new remainder 56, and apply the division lemma to get
259 = 56 x 4 + 35
We consider the new divisor 56 and the new remainder 35,and apply the division lemma to get
56 = 35 x 1 + 21
We consider the new divisor 35 and the new remainder 21,and apply the division lemma to get
35 = 21 x 1 + 14
We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get
21 = 14 x 1 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 574 and 1407 is 7
Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(35,21) = HCF(56,35) = HCF(259,56) = HCF(574,259) = HCF(1407,574) .
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Frequently Asked Questions on HCF of 574, 1407 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, 1407?
Answer: HCF of 574, 1407 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 574, 1407 using Euclid's Algorithm?
Answer: For arbitrary numbers 574, 1407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.