Highest Common Factor of 1470, 8454, 38049 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 1470, 8454, 38049 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1470, 8454, 38049 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 1470, 8454, 38049 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 1470, 8454, 38049 is 3.
HCF(1470, 8454, 38049) = 3
HCF of 1470, 8454, 38049 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1470, 8454, 38049 is 3.
Highest Common Factor of 1470,8454,38049 is 3
Step 1: Since 8454 > 1470, we apply the division lemma to 8454 and 1470, to get
8454 = 1470 x 5 + 1104
Step 2: Since the reminder 1470 ≠ 0, we apply division lemma to 1104 and 1470, to get
1470 = 1104 x 1 + 366
Step 3: We consider the new divisor 1104 and the new remainder 366, and apply the division lemma to get
1104 = 366 x 3 + 6
We consider the new divisor 366 and the new remainder 6, and apply the division lemma to get
366 = 6 x 61 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 1470 and 8454 is 6
Notice that 6 = HCF(366,6) = HCF(1104,366) = HCF(1470,1104) = HCF(8454,1470) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38049 > 6, we apply the division lemma to 38049 and 6, to get
38049 = 6 x 6341 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 38049 is 3
Notice that 3 = HCF(6,3) = HCF(38049,6) .
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Frequently Asked Questions on HCF of 1470, 8454, 38049 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 1470, 8454, 38049?
Answer: HCF of 1470, 8454, 38049 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1470, 8454, 38049 using Euclid's Algorithm?
Answer: For arbitrary numbers 1470, 8454, 38049 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.