Highest Common Factor of 924, 9842 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 924, 9842 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 924, 9842 is 14 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 924, 9842 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 924, 9842 is 14.
HCF(924, 9842) = 14
HCF of 924, 9842 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 924, 9842 is 14.
Highest Common Factor of 924,9842 is 14
Step 1: Since 9842 > 924, we apply the division lemma to 9842 and 924, to get
9842 = 924 x 10 + 602
Step 2: Since the reminder 924 ≠ 0, we apply division lemma to 602 and 924, to get
924 = 602 x 1 + 322
Step 3: We consider the new divisor 602 and the new remainder 322, and apply the division lemma to get
602 = 322 x 1 + 280
We consider the new divisor 322 and the new remainder 280,and apply the division lemma to get
322 = 280 x 1 + 42
We consider the new divisor 280 and the new remainder 42,and apply the division lemma to get
280 = 42 x 6 + 28
We consider the new divisor 42 and the new remainder 28,and apply the division lemma to get
42 = 28 x 1 + 14
We consider the new divisor 28 and the new remainder 14,and apply the division lemma to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 924 and 9842 is 14
Notice that 14 = HCF(28,14) = HCF(42,28) = HCF(280,42) = HCF(322,280) = HCF(602,322) = HCF(924,602) = HCF(9842,924) .
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Frequently Asked Questions on HCF of 924, 9842 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 924, 9842?
Answer: HCF of 924, 9842 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 924, 9842 using Euclid's Algorithm?
Answer: For arbitrary numbers 924, 9842 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.