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 362, 289, 308, 13 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 362, 289, 308, 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 362, 289, 308, 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 362, 289, 308, 13 is 1.
HCF(362, 289, 308, 13) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 362, 289, 308, 13 is 1.
Step 1: Since 362 > 289, we apply the division lemma to 362 and 289, to get
362 = 289 x 1 + 73
Step 2: Since the reminder 289 ≠ 0, we apply division lemma to 73 and 289, to get
289 = 73 x 3 + 70
Step 3: We consider the new divisor 73 and the new remainder 70, and apply the division lemma to get
73 = 70 x 1 + 3
We consider the new divisor 70 and the new remainder 3,and apply the division lemma to get
70 = 3 x 23 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 362 and 289 is 1
Notice that 1 = HCF(3,1) = HCF(70,3) = HCF(73,70) = HCF(289,73) = HCF(362,289) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 308 > 1, we apply the division lemma to 308 and 1, to get
308 = 1 x 308 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 308 is 1
Notice that 1 = HCF(308,1) .
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) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 362, 289, 308, 13?
Answer: HCF of 362, 289, 308, 13 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 362, 289, 308, 13 using Euclid's Algorithm?
Answer: For arbitrary numbers 362, 289, 308, 13 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.