Highest Common Factor of 948, 7008, 2562 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 948, 7008, 2562 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 948, 7008, 2562 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 948, 7008, 2562 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 948, 7008, 2562 is 6.
HCF(948, 7008, 2562) = 6
HCF of 948, 7008, 2562 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 948, 7008, 2562 is 6.
Highest Common Factor of 948,7008,2562 is 6
Step 1: Since 7008 > 948, we apply the division lemma to 7008 and 948, to get
7008 = 948 x 7 + 372
Step 2: Since the reminder 948 ≠ 0, we apply division lemma to 372 and 948, to get
948 = 372 x 2 + 204
Step 3: We consider the new divisor 372 and the new remainder 204, and apply the division lemma to get
372 = 204 x 1 + 168
We consider the new divisor 204 and the new remainder 168,and apply the division lemma to get
204 = 168 x 1 + 36
We consider the new divisor 168 and the new remainder 36,and apply the division lemma to get
168 = 36 x 4 + 24
We consider the new divisor 36 and the new remainder 24,and apply the division lemma to get
36 = 24 x 1 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 948 and 7008 is 12
Notice that 12 = HCF(24,12) = HCF(36,24) = HCF(168,36) = HCF(204,168) = HCF(372,204) = HCF(948,372) = HCF(7008,948) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2562 > 12, we apply the division lemma to 2562 and 12, to get
2562 = 12 x 213 + 6
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 6 and 12, 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 12 and 2562 is 6
Notice that 6 = HCF(12,6) = HCF(2562,12) .
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Frequently Asked Questions on HCF of 948, 7008, 2562 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 948, 7008, 2562?
Answer: HCF of 948, 7008, 2562 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 948, 7008, 2562 using Euclid's Algorithm?
Answer: For arbitrary numbers 948, 7008, 2562 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.