Highest Common Factor of 9648, 470 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 9648, 470 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9648, 470 is 2 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 9648, 470 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 9648, 470 is 2.
HCF(9648, 470) = 2
HCF of 9648, 470 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9648, 470 is 2.
Highest Common Factor of 9648,470 is 2
Step 1: Since 9648 > 470, we apply the division lemma to 9648 and 470, to get
9648 = 470 x 20 + 248
Step 2: Since the reminder 470 ≠ 0, we apply division lemma to 248 and 470, to get
470 = 248 x 1 + 222
Step 3: We consider the new divisor 248 and the new remainder 222, and apply the division lemma to get
248 = 222 x 1 + 26
We consider the new divisor 222 and the new remainder 26,and apply the division lemma to get
222 = 26 x 8 + 14
We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get
26 = 14 x 1 + 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 9648 and 470 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(222,26) = HCF(248,222) = HCF(470,248) = HCF(9648,470) .
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Frequently Asked Questions on HCF of 9648, 470 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 9648, 470?
Answer: HCF of 9648, 470 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9648, 470 using Euclid's Algorithm?
Answer: For arbitrary numbers 9648, 470 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.