Highest Common Factor of 553, 3174 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 553, 3174 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 553, 3174 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 553, 3174 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 553, 3174 is 1.
HCF(553, 3174) = 1
HCF of 553, 3174 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 553, 3174 is 1.
Highest Common Factor of 553,3174 is 1
Step 1: Since 3174 > 553, we apply the division lemma to 3174 and 553, to get
3174 = 553 x 5 + 409
Step 2: Since the reminder 553 ≠ 0, we apply division lemma to 409 and 553, to get
553 = 409 x 1 + 144
Step 3: We consider the new divisor 409 and the new remainder 144, and apply the division lemma to get
409 = 144 x 2 + 121
We consider the new divisor 144 and the new remainder 121,and apply the division lemma to get
144 = 121 x 1 + 23
We consider the new divisor 121 and the new remainder 23,and apply the division lemma to get
121 = 23 x 5 + 6
We consider the new divisor 23 and the new remainder 6,and apply the division lemma to get
23 = 6 x 3 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 553 and 3174 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(23,6) = HCF(121,23) = HCF(144,121) = HCF(409,144) = HCF(553,409) = HCF(3174,553) .
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Frequently Asked Questions on HCF of 553, 3174 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 553, 3174?
Answer: HCF of 553, 3174 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 553, 3174 using Euclid's Algorithm?
Answer: For arbitrary numbers 553, 3174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.