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 316, 522, 975 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 316, 522, 975 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 316, 522, 975 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 316, 522, 975 is 1.
HCF(316, 522, 975) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 316, 522, 975 is 1.
Step 1: Since 522 > 316, we apply the division lemma to 522 and 316, to get
522 = 316 x 1 + 206
Step 2: Since the reminder 316 ≠ 0, we apply division lemma to 206 and 316, to get
316 = 206 x 1 + 110
Step 3: We consider the new divisor 206 and the new remainder 110, and apply the division lemma to get
206 = 110 x 1 + 96
We consider the new divisor 110 and the new remainder 96,and apply the division lemma to get
110 = 96 x 1 + 14
We consider the new divisor 96 and the new remainder 14,and apply the division lemma to get
96 = 14 x 6 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 316 and 522 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(96,14) = HCF(110,96) = HCF(206,110) = HCF(316,206) = HCF(522,316) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 975 > 2, we apply the division lemma to 975 and 2, to get
975 = 2 x 487 + 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 975 is 1
Notice that 1 = HCF(2,1) = HCF(975,2) .
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 316, 522, 975?
Answer: HCF of 316, 522, 975 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 316, 522, 975 using Euclid's Algorithm?
Answer: For arbitrary numbers 316, 522, 975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.