Highest Common Factor of 1686, 1929 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 1686, 1929 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1686, 1929 is 3 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 1686, 1929 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 1686, 1929 is 3.
HCF(1686, 1929) = 3
HCF of 1686, 1929 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1686, 1929 is 3.
Highest Common Factor of 1686,1929 is 3
Step 1: Since 1929 > 1686, we apply the division lemma to 1929 and 1686, to get
1929 = 1686 x 1 + 243
Step 2: Since the reminder 1686 ≠ 0, we apply division lemma to 243 and 1686, to get
1686 = 243 x 6 + 228
Step 3: We consider the new divisor 243 and the new remainder 228, and apply the division lemma to get
243 = 228 x 1 + 15
We consider the new divisor 228 and the new remainder 15,and apply the division lemma to get
228 = 15 x 15 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1686 and 1929 is 3
Notice that 3 = HCF(15,3) = HCF(228,15) = HCF(243,228) = HCF(1686,243) = HCF(1929,1686) .
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Frequently Asked Questions on HCF of 1686, 1929 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 1686, 1929?
Answer: HCF of 1686, 1929 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1686, 1929 using Euclid's Algorithm?
Answer: For arbitrary numbers 1686, 1929 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.