Highest Common Factor of 802, 2060 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 802, 2060 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 802, 2060 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 802, 2060 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 802, 2060 is 2.
HCF(802, 2060) = 2
HCF of 802, 2060 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 802, 2060 is 2.
Highest Common Factor of 802,2060 is 2
Step 1: Since 2060 > 802, we apply the division lemma to 2060 and 802, to get
2060 = 802 x 2 + 456
Step 2: Since the reminder 802 ≠ 0, we apply division lemma to 456 and 802, to get
802 = 456 x 1 + 346
Step 3: We consider the new divisor 456 and the new remainder 346, and apply the division lemma to get
456 = 346 x 1 + 110
We consider the new divisor 346 and the new remainder 110,and apply the division lemma to get
346 = 110 x 3 + 16
We consider the new divisor 110 and the new remainder 16,and apply the division lemma to get
110 = 16 x 6 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 802 and 2060 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(110,16) = HCF(346,110) = HCF(456,346) = HCF(802,456) = HCF(2060,802) .
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Frequently Asked Questions on HCF of 802, 2060 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 802, 2060?
Answer: HCF of 802, 2060 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 802, 2060 using Euclid's Algorithm?
Answer: For arbitrary numbers 802, 2060 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
