Highest Common Factor of 338, 442, 693, 15 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 338, 442, 693, 15 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 338, 442, 693, 15 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 338, 442, 693, 15 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 338, 442, 693, 15 is 1.
HCF(338, 442, 693, 15) = 1
HCF of 338, 442, 693, 15 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 338, 442, 693, 15 is 1.
Highest Common Factor of 338,442,693,15 is 1
Step 1: Since 442 > 338, we apply the division lemma to 442 and 338, to get
442 = 338 x 1 + 104
Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 104 and 338, to get
338 = 104 x 3 + 26
Step 3: We consider the new divisor 104 and the new remainder 26, and apply the division lemma to get
104 = 26 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 338 and 442 is 26
Notice that 26 = HCF(104,26) = HCF(338,104) = HCF(442,338) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 693 > 26, we apply the division lemma to 693 and 26, to get
693 = 26 x 26 + 17
Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 17 and 26, to get
26 = 17 x 1 + 9
Step 3: We consider the new divisor 17 and the new remainder 9, and apply the division lemma to get
17 = 9 x 1 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 26 and 693 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(26,17) = HCF(693,26) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 15 > 1, we apply the division lemma to 15 and 1, to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 15 is 1
Notice that 1 = HCF(15,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 338, 442, 693, 15 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 338, 442, 693, 15?
Answer: HCF of 338, 442, 693, 15 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 338, 442, 693, 15 using Euclid's Algorithm?
Answer: For arbitrary numbers 338, 442, 693, 15 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.