Highest Common Factor of 758, 25342 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 758, 25342 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 758, 25342 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 758, 25342 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 758, 25342 is 2.
HCF(758, 25342) = 2
HCF of 758, 25342 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 758, 25342 is 2.
Highest Common Factor of 758,25342 is 2
Step 1: Since 25342 > 758, we apply the division lemma to 25342 and 758, to get
25342 = 758 x 33 + 328
Step 2: Since the reminder 758 ≠ 0, we apply division lemma to 328 and 758, to get
758 = 328 x 2 + 102
Step 3: We consider the new divisor 328 and the new remainder 102, and apply the division lemma to get
328 = 102 x 3 + 22
We consider the new divisor 102 and the new remainder 22,and apply the division lemma to get
102 = 22 x 4 + 14
We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 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 758 and 25342 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(102,22) = HCF(328,102) = HCF(758,328) = HCF(25342,758) .
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Frequently Asked Questions on HCF of 758, 25342 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 758, 25342?
Answer: HCF of 758, 25342 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 758, 25342 using Euclid's Algorithm?
Answer: For arbitrary numbers 758, 25342 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.