Highest Common Factor of 306, 776, 456, 27 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 306, 776, 456, 27 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 306, 776, 456, 27 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 306, 776, 456, 27 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 306, 776, 456, 27 is 1.
HCF(306, 776, 456, 27) = 1
HCF of 306, 776, 456, 27 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 306, 776, 456, 27 is 1.
Highest Common Factor of 306,776,456,27 is 1
Step 1: Since 776 > 306, we apply the division lemma to 776 and 306, to get
776 = 306 x 2 + 164
Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 164 and 306, to get
306 = 164 x 1 + 142
Step 3: We consider the new divisor 164 and the new remainder 142, and apply the division lemma to get
164 = 142 x 1 + 22
We consider the new divisor 142 and the new remainder 22,and apply the division lemma to get
142 = 22 x 6 + 10
We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get
22 = 10 x 2 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 306 and 776 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(142,22) = HCF(164,142) = HCF(306,164) = HCF(776,306) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 456 > 2, we apply the division lemma to 456 and 2, to get
456 = 2 x 228 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 456 is 2
Notice that 2 = HCF(456,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 27 > 2, we apply the division lemma to 27 and 2, to get
27 = 2 x 13 + 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 27 is 1
Notice that 1 = HCF(2,1) = HCF(27,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 306, 776, 456, 27 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 306, 776, 456, 27?
Answer: HCF of 306, 776, 456, 27 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 306, 776, 456, 27 using Euclid's Algorithm?
Answer: For arbitrary numbers 306, 776, 456, 27 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.