Highest Common Factor of 462, 752 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 462, 752 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 462, 752 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 462, 752 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 462, 752 is 2.
HCF(462, 752) = 2
HCF of 462, 752 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 462, 752 is 2.
Highest Common Factor of 462,752 is 2
Step 1: Since 752 > 462, we apply the division lemma to 752 and 462, to get
752 = 462 x 1 + 290
Step 2: Since the reminder 462 ≠ 0, we apply division lemma to 290 and 462, to get
462 = 290 x 1 + 172
Step 3: We consider the new divisor 290 and the new remainder 172, and apply the division lemma to get
290 = 172 x 1 + 118
We consider the new divisor 172 and the new remainder 118,and apply the division lemma to get
172 = 118 x 1 + 54
We consider the new divisor 118 and the new remainder 54,and apply the division lemma to get
118 = 54 x 2 + 10
We consider the new divisor 54 and the new remainder 10,and apply the division lemma to get
54 = 10 x 5 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 462 and 752 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(54,10) = HCF(118,54) = HCF(172,118) = HCF(290,172) = HCF(462,290) = HCF(752,462) .
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Frequently Asked Questions on HCF of 462, 752 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 462, 752?
Answer: HCF of 462, 752 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 462, 752 using Euclid's Algorithm?
Answer: For arbitrary numbers 462, 752 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.