Highest Common Factor of 8402, 257 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 8402, 257 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8402, 257 is 1 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 8402, 257 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 8402, 257 is 1.
HCF(8402, 257) = 1
HCF of 8402, 257 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8402, 257 is 1.
Highest Common Factor of 8402,257 is 1
Step 1: Since 8402 > 257, we apply the division lemma to 8402 and 257, to get
8402 = 257 x 32 + 178
Step 2: Since the reminder 257 ≠ 0, we apply division lemma to 178 and 257, to get
257 = 178 x 1 + 79
Step 3: We consider the new divisor 178 and the new remainder 79, and apply the division lemma to get
178 = 79 x 2 + 20
We consider the new divisor 79 and the new remainder 20,and apply the division lemma to get
79 = 20 x 3 + 19
We consider the new divisor 20 and the new remainder 19,and apply the division lemma to get
20 = 19 x 1 + 1
We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8402 and 257 is 1
Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(79,20) = HCF(178,79) = HCF(257,178) = HCF(8402,257) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 8402, 257 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 8402, 257?
Answer: HCF of 8402, 257 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8402, 257 using Euclid's Algorithm?
Answer: For arbitrary numbers 8402, 257 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
