Highest Common Factor of 456, 171, 320 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 456, 171, 320 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 456, 171, 320 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 456, 171, 320 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 456, 171, 320 is 1.
HCF(456, 171, 320) = 1
HCF of 456, 171, 320 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 456, 171, 320 is 1.
Highest Common Factor of 456,171,320 is 1
Step 1: Since 456 > 171, we apply the division lemma to 456 and 171, to get
456 = 171 x 2 + 114
Step 2: Since the reminder 171 ≠ 0, we apply division lemma to 114 and 171, to get
171 = 114 x 1 + 57
Step 3: We consider the new divisor 114 and the new remainder 57, and apply the division lemma to get
114 = 57 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 57, the HCF of 456 and 171 is 57
Notice that 57 = HCF(114,57) = HCF(171,114) = HCF(456,171) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 320 > 57, we apply the division lemma to 320 and 57, to get
320 = 57 x 5 + 35
Step 2: Since the reminder 57 ≠ 0, we apply division lemma to 35 and 57, to get
57 = 35 x 1 + 22
Step 3: We consider the new divisor 35 and the new remainder 22, and apply the division lemma to get
35 = 22 x 1 + 13
We consider the new divisor 22 and the new remainder 13,and apply the division lemma to get
22 = 13 x 1 + 9
We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get
13 = 9 x 1 + 4
We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get
9 = 4 x 2 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 57 and 320 is 1
Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(22,13) = HCF(35,22) = HCF(57,35) = HCF(320,57) .
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Frequently Asked Questions on HCF of 456, 171, 320 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 456, 171, 320?
Answer: HCF of 456, 171, 320 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 456, 171, 320 using Euclid's Algorithm?
Answer: For arbitrary numbers 456, 171, 320 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
