Highest Common Factor of 764, 13478 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 764, 13478 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 764, 13478 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 764, 13478 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 764, 13478 is 2.
HCF(764, 13478) = 2
HCF of 764, 13478 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 764, 13478 is 2.
Highest Common Factor of 764,13478 is 2
Step 1: Since 13478 > 764, we apply the division lemma to 13478 and 764, to get
13478 = 764 x 17 + 490
Step 2: Since the reminder 764 ≠ 0, we apply division lemma to 490 and 764, to get
764 = 490 x 1 + 274
Step 3: We consider the new divisor 490 and the new remainder 274, and apply the division lemma to get
490 = 274 x 1 + 216
We consider the new divisor 274 and the new remainder 216,and apply the division lemma to get
274 = 216 x 1 + 58
We consider the new divisor 216 and the new remainder 58,and apply the division lemma to get
216 = 58 x 3 + 42
We consider the new divisor 58 and the new remainder 42,and apply the division lemma to get
58 = 42 x 1 + 16
We consider the new divisor 42 and the new remainder 16,and apply the division lemma to get
42 = 16 x 2 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 764 and 13478 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(42,16) = HCF(58,42) = HCF(216,58) = HCF(274,216) = HCF(490,274) = HCF(764,490) = HCF(13478,764) .
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Frequently Asked Questions on HCF of 764, 13478 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 764, 13478?
Answer: HCF of 764, 13478 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 764, 13478 using Euclid's Algorithm?
Answer: For arbitrary numbers 764, 13478 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
