Highest Common Factor of 8357, 9074 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 8357, 9074 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8357, 9074 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 8357, 9074 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 8357, 9074 is 1.
HCF(8357, 9074) = 1
HCF of 8357, 9074 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8357, 9074 is 1.
Highest Common Factor of 8357,9074 is 1
Step 1: Since 9074 > 8357, we apply the division lemma to 9074 and 8357, to get
9074 = 8357 x 1 + 717
Step 2: Since the reminder 8357 ≠ 0, we apply division lemma to 717 and 8357, to get
8357 = 717 x 11 + 470
Step 3: We consider the new divisor 717 and the new remainder 470, and apply the division lemma to get
717 = 470 x 1 + 247
We consider the new divisor 470 and the new remainder 247,and apply the division lemma to get
470 = 247 x 1 + 223
We consider the new divisor 247 and the new remainder 223,and apply the division lemma to get
247 = 223 x 1 + 24
We consider the new divisor 223 and the new remainder 24,and apply the division lemma to get
223 = 24 x 9 + 7
We consider the new divisor 24 and the new remainder 7,and apply the division lemma to get
24 = 7 x 3 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8357 and 9074 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(24,7) = HCF(223,24) = HCF(247,223) = HCF(470,247) = HCF(717,470) = HCF(8357,717) = HCF(9074,8357) .
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Frequently Asked Questions on HCF of 8357, 9074 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 8357, 9074?
Answer: HCF of 8357, 9074 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8357, 9074 using Euclid's Algorithm?
Answer: For arbitrary numbers 8357, 9074 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.