Highest Common Factor of 2178, 1009 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 2178, 1009 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2178, 1009 is 1 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 2178, 1009 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 2178, 1009 is 1.
HCF(2178, 1009) = 1
HCF of 2178, 1009 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2178, 1009 is 1.
Highest Common Factor of 2178,1009 is 1
Step 1: Since 2178 > 1009, we apply the division lemma to 2178 and 1009, to get
2178 = 1009 x 2 + 160
Step 2: Since the reminder 1009 ≠ 0, we apply division lemma to 160 and 1009, to get
1009 = 160 x 6 + 49
Step 3: We consider the new divisor 160 and the new remainder 49, and apply the division lemma to get
160 = 49 x 3 + 13
We consider the new divisor 49 and the new remainder 13,and apply the division lemma to get
49 = 13 x 3 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2178 and 1009 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(49,13) = HCF(160,49) = HCF(1009,160) = HCF(2178,1009) .
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Frequently Asked Questions on HCF of 2178, 1009 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 2178, 1009?
Answer: HCF of 2178, 1009 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2178, 1009 using Euclid's Algorithm?
Answer: For arbitrary numbers 2178, 1009 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
