Highest Common Factor of 509, 377, 554 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 509, 377, 554 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 509, 377, 554 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 509, 377, 554 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 509, 377, 554 is 1.
HCF(509, 377, 554) = 1
HCF of 509, 377, 554 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 509, 377, 554 is 1.
Highest Common Factor of 509,377,554 is 1
Step 1: Since 509 > 377, we apply the division lemma to 509 and 377, to get
509 = 377 x 1 + 132
Step 2: Since the reminder 377 ≠ 0, we apply division lemma to 132 and 377, to get
377 = 132 x 2 + 113
Step 3: We consider the new divisor 132 and the new remainder 113, and apply the division lemma to get
132 = 113 x 1 + 19
We consider the new divisor 113 and the new remainder 19,and apply the division lemma to get
113 = 19 x 5 + 18
We consider the new divisor 19 and the new remainder 18,and apply the division lemma to get
19 = 18 x 1 + 1
We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get
18 = 1 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 509 and 377 is 1
Notice that 1 = HCF(18,1) = HCF(19,18) = HCF(113,19) = HCF(132,113) = HCF(377,132) = HCF(509,377) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 554 > 1, we apply the division lemma to 554 and 1, to get
554 = 1 x 554 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 554 is 1
Notice that 1 = HCF(554,1) .
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Frequently Asked Questions on HCF of 509, 377, 554 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 509, 377, 554?
Answer: HCF of 509, 377, 554 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 509, 377, 554 using Euclid's Algorithm?
Answer: For arbitrary numbers 509, 377, 554 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.