Highest Common Factor of 852, 699, 312 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 852, 699, 312 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 852, 699, 312 is 3 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 852, 699, 312 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 852, 699, 312 is 3.
HCF(852, 699, 312) = 3
HCF of 852, 699, 312 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 852, 699, 312 is 3.
Highest Common Factor of 852,699,312 is 3
Step 1: Since 852 > 699, we apply the division lemma to 852 and 699, to get
852 = 699 x 1 + 153
Step 2: Since the reminder 699 ≠ 0, we apply division lemma to 153 and 699, to get
699 = 153 x 4 + 87
Step 3: We consider the new divisor 153 and the new remainder 87, and apply the division lemma to get
153 = 87 x 1 + 66
We consider the new divisor 87 and the new remainder 66,and apply the division lemma to get
87 = 66 x 1 + 21
We consider the new divisor 66 and the new remainder 21,and apply the division lemma to get
66 = 21 x 3 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 852 and 699 is 3
Notice that 3 = HCF(21,3) = HCF(66,21) = HCF(87,66) = HCF(153,87) = HCF(699,153) = HCF(852,699) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 312 > 3, we apply the division lemma to 312 and 3, to get
312 = 3 x 104 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 312 is 3
Notice that 3 = HCF(312,3) .
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Frequently Asked Questions on HCF of 852, 699, 312 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 852, 699, 312?
Answer: HCF of 852, 699, 312 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 852, 699, 312 using Euclid's Algorithm?
Answer: For arbitrary numbers 852, 699, 312 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
