Highest Common Factor of 754, 462 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 754, 462 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 754, 462 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 754, 462 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 754, 462 is 2.
HCF(754, 462) = 2
HCF of 754, 462 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 754, 462 is 2.
Highest Common Factor of 754,462 is 2
Step 1: Since 754 > 462, we apply the division lemma to 754 and 462, to get
754 = 462 x 1 + 292
Step 2: Since the reminder 462 ≠ 0, we apply division lemma to 292 and 462, to get
462 = 292 x 1 + 170
Step 3: We consider the new divisor 292 and the new remainder 170, and apply the division lemma to get
292 = 170 x 1 + 122
We consider the new divisor 170 and the new remainder 122,and apply the division lemma to get
170 = 122 x 1 + 48
We consider the new divisor 122 and the new remainder 48,and apply the division lemma to get
122 = 48 x 2 + 26
We consider the new divisor 48 and the new remainder 26,and apply the division lemma to get
48 = 26 x 1 + 22
We consider the new divisor 26 and the new remainder 22,and apply the division lemma to get
26 = 22 x 1 + 4
We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get
22 = 4 x 5 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 754 and 462 is 2
Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(26,22) = HCF(48,26) = HCF(122,48) = HCF(170,122) = HCF(292,170) = HCF(462,292) = HCF(754,462) .
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Frequently Asked Questions on HCF of 754, 462 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 754, 462?
Answer: HCF of 754, 462 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 754, 462 using Euclid's Algorithm?
Answer: For arbitrary numbers 754, 462 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.