Highest Common Factor of 470, 1402 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 470, 1402 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 470, 1402 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 470, 1402 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 470, 1402 is 2.
HCF(470, 1402) = 2
HCF of 470, 1402 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 470, 1402 is 2.
Highest Common Factor of 470,1402 is 2
Step 1: Since 1402 > 470, we apply the division lemma to 1402 and 470, to get
1402 = 470 x 2 + 462
Step 2: Since the reminder 470 ≠ 0, we apply division lemma to 462 and 470, to get
470 = 462 x 1 + 8
Step 3: We consider the new divisor 462 and the new remainder 8, and apply the division lemma to get
462 = 8 x 57 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 470 and 1402 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(462,8) = HCF(470,462) = HCF(1402,470) .
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Frequently Asked Questions on HCF of 470, 1402 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 470, 1402?
Answer: HCF of 470, 1402 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 470, 1402 using Euclid's Algorithm?
Answer: For arbitrary numbers 470, 1402 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.