Highest Common Factor of 852, 564, 909, 825 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, 564, 909, 825 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 852, 564, 909, 825 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, 564, 909, 825 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, 564, 909, 825 is 3.
HCF(852, 564, 909, 825) = 3
HCF of 852, 564, 909, 825 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, 564, 909, 825 is 3.
Highest Common Factor of 852,564,909,825 is 3
Step 1: Since 852 > 564, we apply the division lemma to 852 and 564, to get
852 = 564 x 1 + 288
Step 2: Since the reminder 564 ≠ 0, we apply division lemma to 288 and 564, to get
564 = 288 x 1 + 276
Step 3: We consider the new divisor 288 and the new remainder 276, and apply the division lemma to get
288 = 276 x 1 + 12
We consider the new divisor 276 and the new remainder 12, and apply the division lemma to get
276 = 12 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 852 and 564 is 12
Notice that 12 = HCF(276,12) = HCF(288,276) = HCF(564,288) = HCF(852,564) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 909 > 12, we apply the division lemma to 909 and 12, to get
909 = 12 x 75 + 9
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 9 and 12, to get
12 = 9 x 1 + 3
Step 3: We consider the new divisor 9 and the new remainder 3, and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 12 and 909 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(909,12) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 825 > 3, we apply the division lemma to 825 and 3, to get
825 = 3 x 275 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 825 is 3
Notice that 3 = HCF(825,3) .
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Frequently Asked Questions on HCF of 852, 564, 909, 825 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, 564, 909, 825?
Answer: HCF of 852, 564, 909, 825 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 852, 564, 909, 825 using Euclid's Algorithm?
Answer: For arbitrary numbers 852, 564, 909, 825 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.