Highest Common Factor of 970, 578 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 970, 578 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 970, 578 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 970, 578 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 970, 578 is 2.
HCF(970, 578) = 2
HCF of 970, 578 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 970, 578 is 2.
Highest Common Factor of 970,578 is 2
Step 1: Since 970 > 578, we apply the division lemma to 970 and 578, to get
970 = 578 x 1 + 392
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 392 and 578, to get
578 = 392 x 1 + 186
Step 3: We consider the new divisor 392 and the new remainder 186, and apply the division lemma to get
392 = 186 x 2 + 20
We consider the new divisor 186 and the new remainder 20,and apply the division lemma to get
186 = 20 x 9 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 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 970 and 578 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(186,20) = HCF(392,186) = HCF(578,392) = HCF(970,578) .
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Frequently Asked Questions on HCF of 970, 578 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 970, 578?
Answer: HCF of 970, 578 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 970, 578 using Euclid's Algorithm?
Answer: For arbitrary numbers 970, 578 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.