Highest Common Factor of 255, 942, 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 255, 942, 13 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 255, 942, 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 255, 942, 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 255, 942, 13 is 1.
HCF(255, 942, 13) = 1
HCF of 255, 942, 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 255, 942, 13 is 1.
Highest Common Factor of 255,942,13 is 1
Step 1: Since 942 > 255, we apply the division lemma to 942 and 255, to get
942 = 255 x 3 + 177
Step 2: Since the reminder 255 ≠ 0, we apply division lemma to 177 and 255, to get
255 = 177 x 1 + 78
Step 3: We consider the new divisor 177 and the new remainder 78, and apply the division lemma to get
177 = 78 x 2 + 21
We consider the new divisor 78 and the new remainder 21,and apply the division lemma to get
78 = 21 x 3 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 255 and 942 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(78,21) = HCF(177,78) = HCF(255,177) = HCF(942,255) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 13 > 3, we apply the division lemma to 13 and 3, to get
13 = 3 x 4 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 13 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) .
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Frequently Asked Questions on HCF of 255, 942, 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 255, 942, 13?
Answer: HCF of 255, 942, 13 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 255, 942, 13 using Euclid's Algorithm?
Answer: For arbitrary numbers 255, 942, 13 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.