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 349, 608, 388, 45 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 349, 608, 388, 45 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 349, 608, 388, 45 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 349, 608, 388, 45 is 1.
HCF(349, 608, 388, 45) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 349, 608, 388, 45 is 1.
Step 1: Since 608 > 349, we apply the division lemma to 608 and 349, to get
608 = 349 x 1 + 259
Step 2: Since the reminder 349 ≠ 0, we apply division lemma to 259 and 349, to get
349 = 259 x 1 + 90
Step 3: We consider the new divisor 259 and the new remainder 90, and apply the division lemma to get
259 = 90 x 2 + 79
We consider the new divisor 90 and the new remainder 79,and apply the division lemma to get
90 = 79 x 1 + 11
We consider the new divisor 79 and the new remainder 11,and apply the division lemma to get
79 = 11 x 7 + 2
We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get
11 = 2 x 5 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 349 and 608 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(79,11) = HCF(90,79) = HCF(259,90) = HCF(349,259) = HCF(608,349) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 388 > 1, we apply the division lemma to 388 and 1, to get
388 = 1 x 388 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 388 is 1
Notice that 1 = HCF(388,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45 > 1, we apply the division lemma to 45 and 1, to get
45 = 1 x 45 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 45 is 1
Notice that 1 = HCF(45,1) .
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 349, 608, 388, 45?
Answer: HCF of 349, 608, 388, 45 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 349, 608, 388, 45 using Euclid's Algorithm?
Answer: For arbitrary numbers 349, 608, 388, 45 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.