Highest Common Factor of 523, 160, 392, 654 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 523, 160, 392, 654 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 523, 160, 392, 654 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 523, 160, 392, 654 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 523, 160, 392, 654 is 1.
HCF(523, 160, 392, 654) = 1
HCF of 523, 160, 392, 654 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 523, 160, 392, 654 is 1.
Highest Common Factor of 523,160,392,654 is 1
Step 1: Since 523 > 160, we apply the division lemma to 523 and 160, to get
523 = 160 x 3 + 43
Step 2: Since the reminder 160 ≠ 0, we apply division lemma to 43 and 160, to get
160 = 43 x 3 + 31
Step 3: We consider the new divisor 43 and the new remainder 31, and apply the division lemma to get
43 = 31 x 1 + 12
We consider the new divisor 31 and the new remainder 12,and apply the division lemma to get
31 = 12 x 2 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 523 and 160 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(31,12) = HCF(43,31) = HCF(160,43) = HCF(523,160) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 392 > 1, we apply the division lemma to 392 and 1, to get
392 = 1 x 392 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 392 is 1
Notice that 1 = HCF(392,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 654 > 1, we apply the division lemma to 654 and 1, to get
654 = 1 x 654 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 654 is 1
Notice that 1 = HCF(654,1) .
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Frequently Asked Questions on HCF of 523, 160, 392, 654 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 523, 160, 392, 654?
Answer: HCF of 523, 160, 392, 654 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 523, 160, 392, 654 using Euclid's Algorithm?
Answer: For arbitrary numbers 523, 160, 392, 654 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.