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 491, 377, 118 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 491, 377, 118 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 491, 377, 118 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 491, 377, 118 is 1.
HCF(491, 377, 118) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 491, 377, 118 is 1.
Step 1: Since 491 > 377, we apply the division lemma to 491 and 377, to get
491 = 377 x 1 + 114
Step 2: Since the reminder 377 ≠ 0, we apply division lemma to 114 and 377, to get
377 = 114 x 3 + 35
Step 3: We consider the new divisor 114 and the new remainder 35, and apply the division lemma to get
114 = 35 x 3 + 9
We consider the new divisor 35 and the new remainder 9,and apply the division lemma to get
35 = 9 x 3 + 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 491 and 377 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(35,9) = HCF(114,35) = HCF(377,114) = HCF(491,377) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 118 > 1, we apply the division lemma to 118 and 1, to get
118 = 1 x 118 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 118 is 1
Notice that 1 = HCF(118,1) .
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 491, 377, 118?
Answer: HCF of 491, 377, 118 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 491, 377, 118 using Euclid's Algorithm?
Answer: For arbitrary numbers 491, 377, 118 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.