Highest Common Factor of 720, 164, 105, 260 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 720, 164, 105, 260 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 720, 164, 105, 260 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 720, 164, 105, 260 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 720, 164, 105, 260 is 1.
HCF(720, 164, 105, 260) = 1
HCF of 720, 164, 105, 260 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 720, 164, 105, 260 is 1.
Highest Common Factor of 720,164,105,260 is 1
Step 1: Since 720 > 164, we apply the division lemma to 720 and 164, to get
720 = 164 x 4 + 64
Step 2: Since the reminder 164 ≠ 0, we apply division lemma to 64 and 164, to get
164 = 64 x 2 + 36
Step 3: We consider the new divisor 64 and the new remainder 36, and apply the division lemma to get
64 = 36 x 1 + 28
We consider the new divisor 36 and the new remainder 28,and apply the division lemma to get
36 = 28 x 1 + 8
We consider the new divisor 28 and the new remainder 8,and apply the division lemma to get
28 = 8 x 3 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 720 and 164 is 4
Notice that 4 = HCF(8,4) = HCF(28,8) = HCF(36,28) = HCF(64,36) = HCF(164,64) = HCF(720,164) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 4, we apply the division lemma to 105 and 4, to get
105 = 4 x 26 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 105 is 1
Notice that 1 = HCF(4,1) = HCF(105,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 260 > 1, we apply the division lemma to 260 and 1, to get
260 = 1 x 260 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 260 is 1
Notice that 1 = HCF(260,1) .
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Frequently Asked Questions on HCF of 720, 164, 105, 260 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 720, 164, 105, 260?
Answer: HCF of 720, 164, 105, 260 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 720, 164, 105, 260 using Euclid's Algorithm?
Answer: For arbitrary numbers 720, 164, 105, 260 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.