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 671, 416, 49 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 671, 416, 49 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 671, 416, 49 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 671, 416, 49 is 1.
HCF(671, 416, 49) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 671, 416, 49 is 1.
Step 1: Since 671 > 416, we apply the division lemma to 671 and 416, to get
671 = 416 x 1 + 255
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 255 and 416, to get
416 = 255 x 1 + 161
Step 3: We consider the new divisor 255 and the new remainder 161, and apply the division lemma to get
255 = 161 x 1 + 94
We consider the new divisor 161 and the new remainder 94,and apply the division lemma to get
161 = 94 x 1 + 67
We consider the new divisor 94 and the new remainder 67,and apply the division lemma to get
94 = 67 x 1 + 27
We consider the new divisor 67 and the new remainder 27,and apply the division lemma to get
67 = 27 x 2 + 13
We consider the new divisor 27 and the new remainder 13,and apply the division lemma to get
27 = 13 x 2 + 1
We consider the new divisor 13 and the new remainder 1,and apply the division lemma 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 671 and 416 is 1
Notice that 1 = HCF(13,1) = HCF(27,13) = HCF(67,27) = HCF(94,67) = HCF(161,94) = HCF(255,161) = HCF(416,255) = HCF(671,416) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 49 > 1, we apply the division lemma to 49 and 1, to get
49 = 1 x 49 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 49 is 1
Notice that 1 = HCF(49,1) .
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 671, 416, 49?
Answer: HCF of 671, 416, 49 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 671, 416, 49 using Euclid's Algorithm?
Answer: For arbitrary numbers 671, 416, 49 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.