Highest Common Factor of 553, 674, 12 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, 674, 12 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 553, 674, 12 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, 674, 12 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, 674, 12 is 1.
HCF(553, 674, 12) = 1
HCF of 553, 674, 12 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, 674, 12 is 1.
Highest Common Factor of 553,674,12 is 1
Step 1: Since 674 > 553, we apply the division lemma to 674 and 553, to get
674 = 553 x 1 + 121
Step 2: Since the reminder 553 ≠ 0, we apply division lemma to 121 and 553, to get
553 = 121 x 4 + 69
Step 3: We consider the new divisor 121 and the new remainder 69, and apply the division lemma to get
121 = 69 x 1 + 52
We consider the new divisor 69 and the new remainder 52,and apply the division lemma to get
69 = 52 x 1 + 17
We consider the new divisor 52 and the new remainder 17,and apply the division lemma to get
52 = 17 x 3 + 1
We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 553 and 674 is 1
Notice that 1 = HCF(17,1) = HCF(52,17) = HCF(69,52) = HCF(121,69) = HCF(553,121) = HCF(674,553) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 12 > 1, we apply the division lemma to 12 and 1, to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 12 is 1
Notice that 1 = HCF(12,1) .
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Frequently Asked Questions on HCF of 553, 674, 12 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, 674, 12?
Answer: HCF of 553, 674, 12 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 553, 674, 12 using Euclid's Algorithm?
Answer: For arbitrary numbers 553, 674, 12 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.