Highest Common Factor of 478, 1688 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 478, 1688 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 478, 1688 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 478, 1688 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 478, 1688 is 2.
HCF(478, 1688) = 2
HCF of 478, 1688 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 478, 1688 is 2.
Highest Common Factor of 478,1688 is 2
Step 1: Since 1688 > 478, we apply the division lemma to 1688 and 478, to get
1688 = 478 x 3 + 254
Step 2: Since the reminder 478 ≠ 0, we apply division lemma to 254 and 478, to get
478 = 254 x 1 + 224
Step 3: We consider the new divisor 254 and the new remainder 224, and apply the division lemma to get
254 = 224 x 1 + 30
We consider the new divisor 224 and the new remainder 30,and apply the division lemma to get
224 = 30 x 7 + 14
We consider the new divisor 30 and the new remainder 14,and apply the division lemma to get
30 = 14 x 2 + 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 478 and 1688 is 2
Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(224,30) = HCF(254,224) = HCF(478,254) = HCF(1688,478) .
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Frequently Asked Questions on HCF of 478, 1688 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 478, 1688?
Answer: HCF of 478, 1688 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 478, 1688 using Euclid's Algorithm?
Answer: For arbitrary numbers 478, 1688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.