Highest Common Factor of 509, 138, 748 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, 138, 748 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 509, 138, 748 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, 138, 748 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, 138, 748 is 1.
HCF(509, 138, 748) = 1
HCF of 509, 138, 748 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, 138, 748 is 1.
Highest Common Factor of 509,138,748 is 1
Step 1: Since 509 > 138, we apply the division lemma to 509 and 138, to get
509 = 138 x 3 + 95
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 95 and 138, to get
138 = 95 x 1 + 43
Step 3: We consider the new divisor 95 and the new remainder 43, and apply the division lemma to get
95 = 43 x 2 + 9
We consider the new divisor 43 and the new remainder 9,and apply the division lemma to get
43 = 9 x 4 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 509 and 138 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(43,9) = HCF(95,43) = HCF(138,95) = HCF(509,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 748 > 1, we apply the division lemma to 748 and 1, to get
748 = 1 x 748 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 748 is 1
Notice that 1 = HCF(748,1) .
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Frequently Asked Questions on HCF of 509, 138, 748 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, 138, 748?
Answer: HCF of 509, 138, 748 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 509, 138, 748 using Euclid's Algorithm?
Answer: For arbitrary numbers 509, 138, 748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
