Highest Common Factor of 1678, 9208 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 1678, 9208 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1678, 9208 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 1678, 9208 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 1678, 9208 is 2.
HCF(1678, 9208) = 2
HCF of 1678, 9208 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1678, 9208 is 2.
Highest Common Factor of 1678,9208 is 2
Step 1: Since 9208 > 1678, we apply the division lemma to 9208 and 1678, to get
9208 = 1678 x 5 + 818
Step 2: Since the reminder 1678 ≠ 0, we apply division lemma to 818 and 1678, to get
1678 = 818 x 2 + 42
Step 3: We consider the new divisor 818 and the new remainder 42, and apply the division lemma to get
818 = 42 x 19 + 20
We consider the new divisor 42 and the new remainder 20,and apply the division lemma to get
42 = 20 x 2 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1678 and 9208 is 2
Notice that 2 = HCF(20,2) = HCF(42,20) = HCF(818,42) = HCF(1678,818) = HCF(9208,1678) .
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Frequently Asked Questions on HCF of 1678, 9208 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 1678, 9208?
Answer: HCF of 1678, 9208 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1678, 9208 using Euclid's Algorithm?
Answer: For arbitrary numbers 1678, 9208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
