Highest Common Factor of 702, 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 702, 578 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 702, 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 702, 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 702, 578 is 2.
HCF(702, 578) = 2
HCF of 702, 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 702, 578 is 2.
Highest Common Factor of 702,578 is 2
Step 1: Since 702 > 578, we apply the division lemma to 702 and 578, to get
702 = 578 x 1 + 124
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 124 and 578, to get
578 = 124 x 4 + 82
Step 3: We consider the new divisor 124 and the new remainder 82, and apply the division lemma to get
124 = 82 x 1 + 42
We consider the new divisor 82 and the new remainder 42,and apply the division lemma to get
82 = 42 x 1 + 40
We consider the new divisor 42 and the new remainder 40,and apply the division lemma to get
42 = 40 x 1 + 2
We consider the new divisor 40 and the new remainder 2,and apply the division lemma to get
40 = 2 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 702 and 578 is 2
Notice that 2 = HCF(40,2) = HCF(42,40) = HCF(82,42) = HCF(124,82) = HCF(578,124) = HCF(702,578) .
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Frequently Asked Questions on HCF of 702, 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 702, 578?
Answer: HCF of 702, 578 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 702, 578 using Euclid's Algorithm?
Answer: For arbitrary numbers 702, 578 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.