Highest Common Factor of 462, 802, 852 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, 802, 852 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 462, 802, 852 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, 802, 852 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, 802, 852 is 2.
HCF(462, 802, 852) = 2
HCF of 462, 802, 852 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, 802, 852 is 2.
Highest Common Factor of 462,802,852 is 2
Step 1: Since 802 > 462, we apply the division lemma to 802 and 462, to get
802 = 462 x 1 + 340
Step 2: Since the reminder 462 ≠ 0, we apply division lemma to 340 and 462, to get
462 = 340 x 1 + 122
Step 3: We consider the new divisor 340 and the new remainder 122, and apply the division lemma to get
340 = 122 x 2 + 96
We consider the new divisor 122 and the new remainder 96,and apply the division lemma to get
122 = 96 x 1 + 26
We consider the new divisor 96 and the new remainder 26,and apply the division lemma to get
96 = 26 x 3 + 18
We consider the new divisor 26 and the new remainder 18,and apply the division lemma to get
26 = 18 x 1 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 462 and 802 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(26,18) = HCF(96,26) = HCF(122,96) = HCF(340,122) = HCF(462,340) = HCF(802,462) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 852 > 2, we apply the division lemma to 852 and 2, to get
852 = 2 x 426 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 852 is 2
Notice that 2 = HCF(852,2) .
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Frequently Asked Questions on HCF of 462, 802, 852 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, 802, 852?
Answer: HCF of 462, 802, 852 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 462, 802, 852 using Euclid's Algorithm?
Answer: For arbitrary numbers 462, 802, 852 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.