Highest Common Factor of 262, 602, 105, 13 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 262, 602, 105, 13 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 262, 602, 105, 13 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 262, 602, 105, 13 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 262, 602, 105, 13 is 1.
HCF(262, 602, 105, 13) = 1
HCF of 262, 602, 105, 13 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 262, 602, 105, 13 is 1.
Highest Common Factor of 262,602,105,13 is 1
Step 1: Since 602 > 262, we apply the division lemma to 602 and 262, to get
602 = 262 x 2 + 78
Step 2: Since the reminder 262 ≠ 0, we apply division lemma to 78 and 262, to get
262 = 78 x 3 + 28
Step 3: We consider the new divisor 78 and the new remainder 28, and apply the division lemma to get
78 = 28 x 2 + 22
We consider the new divisor 28 and the new remainder 22,and apply the division lemma to get
28 = 22 x 1 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 262 and 602 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(78,28) = HCF(262,78) = HCF(602,262) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 2, we apply the division lemma to 105 and 2, to get
105 = 2 x 52 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 105 is 1
Notice that 1 = HCF(2,1) = HCF(105,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 13 > 1, we apply the division lemma to 13 and 1, to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 13 is 1
Notice that 1 = HCF(13,1) .
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Frequently Asked Questions on HCF of 262, 602, 105, 13 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 262, 602, 105, 13?
Answer: HCF of 262, 602, 105, 13 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 262, 602, 105, 13 using Euclid's Algorithm?
Answer: For arbitrary numbers 262, 602, 105, 13 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.