Highest Common Factor of 946, 488, 31, 965 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 946, 488, 31, 965 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 946, 488, 31, 965 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 946, 488, 31, 965 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 946, 488, 31, 965 is 1.
HCF(946, 488, 31, 965) = 1
HCF of 946, 488, 31, 965 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 946, 488, 31, 965 is 1.
Highest Common Factor of 946,488,31,965 is 1
Step 1: Since 946 > 488, we apply the division lemma to 946 and 488, to get
946 = 488 x 1 + 458
Step 2: Since the reminder 488 ≠ 0, we apply division lemma to 458 and 488, to get
488 = 458 x 1 + 30
Step 3: We consider the new divisor 458 and the new remainder 30, and apply the division lemma to get
458 = 30 x 15 + 8
We consider the new divisor 30 and the new remainder 8,and apply the division lemma to get
30 = 8 x 3 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 946 and 488 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(30,8) = HCF(458,30) = HCF(488,458) = HCF(946,488) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31 > 2, we apply the division lemma to 31 and 2, to get
31 = 2 x 15 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 31 is 1
Notice that 1 = HCF(2,1) = HCF(31,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 965 > 1, we apply the division lemma to 965 and 1, to get
965 = 1 x 965 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 965 is 1
Notice that 1 = HCF(965,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 946, 488, 31, 965 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 946, 488, 31, 965?
Answer: HCF of 946, 488, 31, 965 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 946, 488, 31, 965 using Euclid's Algorithm?
Answer: For arbitrary numbers 946, 488, 31, 965 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.