Highest Common Factor of 420, 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 420, 574 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 574 is 14 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 420, 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 420, 574 is 14.
HCF(420, 574) = 14
HCF of 420, 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 420, 574 is 14.
Highest Common Factor of 420,574 is 14
Step 1: Since 574 > 420, we apply the division lemma to 574 and 420, to get
574 = 420 x 1 + 154
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 154 and 420, to get
420 = 154 x 2 + 112
Step 3: We consider the new divisor 154 and the new remainder 112, and apply the division lemma to get
154 = 112 x 1 + 42
We consider the new divisor 112 and the new remainder 42,and apply the division lemma to get
112 = 42 x 2 + 28
We consider the new divisor 42 and the new remainder 28,and apply the division lemma to get
42 = 28 x 1 + 14
We consider the new divisor 28 and the new remainder 14,and apply the division lemma to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 420 and 574 is 14
Notice that 14 = HCF(28,14) = HCF(42,28) = HCF(112,42) = HCF(154,112) = HCF(420,154) = HCF(574,420) .
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Frequently Asked Questions on HCF of 420, 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 420, 574?
Answer: HCF of 420, 574 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 574 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 574 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.