Highest Common Factor of 1577, 8224 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 1577, 8224 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1577, 8224 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 1577, 8224 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 1577, 8224 is 1.
HCF(1577, 8224) = 1
HCF of 1577, 8224 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1577, 8224 is 1.
Highest Common Factor of 1577,8224 is 1
Step 1: Since 8224 > 1577, we apply the division lemma to 8224 and 1577, to get
8224 = 1577 x 5 + 339
Step 2: Since the reminder 1577 ≠ 0, we apply division lemma to 339 and 1577, to get
1577 = 339 x 4 + 221
Step 3: We consider the new divisor 339 and the new remainder 221, and apply the division lemma to get
339 = 221 x 1 + 118
We consider the new divisor 221 and the new remainder 118,and apply the division lemma to get
221 = 118 x 1 + 103
We consider the new divisor 118 and the new remainder 103,and apply the division lemma to get
118 = 103 x 1 + 15
We consider the new divisor 103 and the new remainder 15,and apply the division lemma to get
103 = 15 x 6 + 13
We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get
15 = 13 x 1 + 2
We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get
13 = 2 x 6 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1577 and 8224 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(103,15) = HCF(118,103) = HCF(221,118) = HCF(339,221) = HCF(1577,339) = HCF(8224,1577) .
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Frequently Asked Questions on HCF of 1577, 8224 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 1577, 8224?
Answer: HCF of 1577, 8224 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1577, 8224 using Euclid's Algorithm?
Answer: For arbitrary numbers 1577, 8224 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
