Highest Common Factor of 988, 77574 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 988, 77574 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 988, 77574 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 988, 77574 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 988, 77574 is 2.
HCF(988, 77574) = 2
HCF of 988, 77574 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 988, 77574 is 2.
Highest Common Factor of 988,77574 is 2
Step 1: Since 77574 > 988, we apply the division lemma to 77574 and 988, to get
77574 = 988 x 78 + 510
Step 2: Since the reminder 988 ≠ 0, we apply division lemma to 510 and 988, to get
988 = 510 x 1 + 478
Step 3: We consider the new divisor 510 and the new remainder 478, and apply the division lemma to get
510 = 478 x 1 + 32
We consider the new divisor 478 and the new remainder 32,and apply the division lemma to get
478 = 32 x 14 + 30
We consider the new divisor 32 and the new remainder 30,and apply the division lemma to get
32 = 30 x 1 + 2
We consider the new divisor 30 and the new remainder 2,and apply the division lemma to get
30 = 2 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 988 and 77574 is 2
Notice that 2 = HCF(30,2) = HCF(32,30) = HCF(478,32) = HCF(510,478) = HCF(988,510) = HCF(77574,988) .
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Frequently Asked Questions on HCF of 988, 77574 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 988, 77574?
Answer: HCF of 988, 77574 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 988, 77574 using Euclid's Algorithm?
Answer: For arbitrary numbers 988, 77574 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.