Highest Common Factor of 992, 7409 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 992, 7409 i.e. 31 the largest integer that leaves a remainder zero for all numbers.
HCF of 992, 7409 is 31 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 992, 7409 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 992, 7409 is 31.
HCF(992, 7409) = 31
HCF of 992, 7409 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 992, 7409 is 31.
Highest Common Factor of 992,7409 is 31
Step 1: Since 7409 > 992, we apply the division lemma to 7409 and 992, to get
7409 = 992 x 7 + 465
Step 2: Since the reminder 992 ≠ 0, we apply division lemma to 465 and 992, to get
992 = 465 x 2 + 62
Step 3: We consider the new divisor 465 and the new remainder 62, and apply the division lemma to get
465 = 62 x 7 + 31
We consider the new divisor 62 and the new remainder 31, and apply the division lemma to get
62 = 31 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 31, the HCF of 992 and 7409 is 31
Notice that 31 = HCF(62,31) = HCF(465,62) = HCF(992,465) = HCF(7409,992) .
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Frequently Asked Questions on HCF of 992, 7409 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 992, 7409?
Answer: HCF of 992, 7409 is 31 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 992, 7409 using Euclid's Algorithm?
Answer: For arbitrary numbers 992, 7409 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.