Highest Common Factor of 145, 704, 123 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 145, 704, 123 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 145, 704, 123 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 145, 704, 123 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 145, 704, 123 is 1.
HCF(145, 704, 123) = 1
HCF of 145, 704, 123 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 145, 704, 123 is 1.
Highest Common Factor of 145,704,123 is 1
Step 1: Since 704 > 145, we apply the division lemma to 704 and 145, to get
704 = 145 x 4 + 124
Step 2: Since the reminder 145 ≠ 0, we apply division lemma to 124 and 145, to get
145 = 124 x 1 + 21
Step 3: We consider the new divisor 124 and the new remainder 21, and apply the division lemma to get
124 = 21 x 5 + 19
We consider the new divisor 21 and the new remainder 19,and apply the division lemma to get
21 = 19 x 1 + 2
We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get
19 = 2 x 9 + 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 145 and 704 is 1
Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(124,21) = HCF(145,124) = HCF(704,145) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 123 > 1, we apply the division lemma to 123 and 1, to get
123 = 1 x 123 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 123 is 1
Notice that 1 = HCF(123,1) .
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Frequently Asked Questions on HCF of 145, 704, 123 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 145, 704, 123?
Answer: HCF of 145, 704, 123 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 145, 704, 123 using Euclid's Algorithm?
Answer: For arbitrary numbers 145, 704, 123 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.