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 916, 350, 953 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 916, 350, 953 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 916, 350, 953 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 916, 350, 953 is 1.
HCF(916, 350, 953) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 916, 350, 953 is 1.
Step 1: Since 916 > 350, we apply the division lemma to 916 and 350, to get
916 = 350 x 2 + 216
Step 2: Since the reminder 350 ≠ 0, we apply division lemma to 216 and 350, to get
350 = 216 x 1 + 134
Step 3: We consider the new divisor 216 and the new remainder 134, and apply the division lemma to get
216 = 134 x 1 + 82
We consider the new divisor 134 and the new remainder 82,and apply the division lemma to get
134 = 82 x 1 + 52
We consider the new divisor 82 and the new remainder 52,and apply the division lemma to get
82 = 52 x 1 + 30
We consider the new divisor 52 and the new remainder 30,and apply the division lemma to get
52 = 30 x 1 + 22
We consider the new divisor 30 and the new remainder 22,and apply the division lemma to get
30 = 22 x 1 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 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 916 and 350 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(30,22) = HCF(52,30) = HCF(82,52) = HCF(134,82) = HCF(216,134) = HCF(350,216) = HCF(916,350) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 953 > 2, we apply the division lemma to 953 and 2, to get
953 = 2 x 476 + 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 953 is 1
Notice that 1 = HCF(2,1) = HCF(953,2) .
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 916, 350, 953?
Answer: HCF of 916, 350, 953 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 916, 350, 953 using Euclid's Algorithm?
Answer: For arbitrary numbers 916, 350, 953 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.