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 712, 416, 349 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 712, 416, 349 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 712, 416, 349 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 712, 416, 349 is 1.
HCF(712, 416, 349) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 712, 416, 349 is 1.
Step 1: Since 712 > 416, we apply the division lemma to 712 and 416, to get
712 = 416 x 1 + 296
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 296 and 416, to get
416 = 296 x 1 + 120
Step 3: We consider the new divisor 296 and the new remainder 120, and apply the division lemma to get
296 = 120 x 2 + 56
We consider the new divisor 120 and the new remainder 56,and apply the division lemma to get
120 = 56 x 2 + 8
We consider the new divisor 56 and the new remainder 8,and apply the division lemma to get
56 = 8 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 712 and 416 is 8
Notice that 8 = HCF(56,8) = HCF(120,56) = HCF(296,120) = HCF(416,296) = HCF(712,416) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 349 > 8, we apply the division lemma to 349 and 8, to get
349 = 8 x 43 + 5
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 5 and 8, to get
8 = 5 x 1 + 3
Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 8 and 349 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(349,8) .
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 712, 416, 349?
Answer: HCF of 712, 416, 349 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 712, 416, 349 using Euclid's Algorithm?
Answer: For arbitrary numbers 712, 416, 349 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.