Highest Common Factor of 852, 2238, 5040 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, 2238, 5040 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 852, 2238, 5040 is 6 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, 2238, 5040 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, 2238, 5040 is 6.
HCF(852, 2238, 5040) = 6
HCF of 852, 2238, 5040 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, 2238, 5040 is 6.
Highest Common Factor of 852,2238,5040 is 6
Step 1: Since 2238 > 852, we apply the division lemma to 2238 and 852, to get
2238 = 852 x 2 + 534
Step 2: Since the reminder 852 ≠ 0, we apply division lemma to 534 and 852, to get
852 = 534 x 1 + 318
Step 3: We consider the new divisor 534 and the new remainder 318, and apply the division lemma to get
534 = 318 x 1 + 216
We consider the new divisor 318 and the new remainder 216,and apply the division lemma to get
318 = 216 x 1 + 102
We consider the new divisor 216 and the new remainder 102,and apply the division lemma to get
216 = 102 x 2 + 12
We consider the new divisor 102 and the new remainder 12,and apply the division lemma to get
102 = 12 x 8 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 852 and 2238 is 6
Notice that 6 = HCF(12,6) = HCF(102,12) = HCF(216,102) = HCF(318,216) = HCF(534,318) = HCF(852,534) = HCF(2238,852) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5040 > 6, we apply the division lemma to 5040 and 6, to get
5040 = 6 x 840 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 5040 is 6
Notice that 6 = HCF(5040,6) .
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Frequently Asked Questions on HCF of 852, 2238, 5040 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, 2238, 5040?
Answer: HCF of 852, 2238, 5040 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 852, 2238, 5040 using Euclid's Algorithm?
Answer: For arbitrary numbers 852, 2238, 5040 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.