Highest Common Factor of 748, 478 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 748, 478 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 748, 478 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 748, 478 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 748, 478 is 2.
HCF(748, 478) = 2
HCF of 748, 478 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 748, 478 is 2.
Highest Common Factor of 748,478 is 2
Step 1: Since 748 > 478, we apply the division lemma to 748 and 478, to get
748 = 478 x 1 + 270
Step 2: Since the reminder 478 ≠ 0, we apply division lemma to 270 and 478, to get
478 = 270 x 1 + 208
Step 3: We consider the new divisor 270 and the new remainder 208, and apply the division lemma to get
270 = 208 x 1 + 62
We consider the new divisor 208 and the new remainder 62,and apply the division lemma to get
208 = 62 x 3 + 22
We consider the new divisor 62 and the new remainder 22,and apply the division lemma to get
62 = 22 x 2 + 18
We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get
22 = 18 x 1 + 4
We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get
18 = 4 x 4 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 748 and 478 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(62,22) = HCF(208,62) = HCF(270,208) = HCF(478,270) = HCF(748,478) .
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Frequently Asked Questions on HCF of 748, 478 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 748, 478?
Answer: HCF of 748, 478 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 748, 478 using Euclid's Algorithm?
Answer: For arbitrary numbers 748, 478 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.