Highest Common Factor of 488, 680, 974 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 488, 680, 974 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 488, 680, 974 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 488, 680, 974 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 488, 680, 974 is 2.
HCF(488, 680, 974) = 2
HCF of 488, 680, 974 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 488, 680, 974 is 2.
Highest Common Factor of 488,680,974 is 2
Step 1: Since 680 > 488, we apply the division lemma to 680 and 488, to get
680 = 488 x 1 + 192
Step 2: Since the reminder 488 ≠ 0, we apply division lemma to 192 and 488, to get
488 = 192 x 2 + 104
Step 3: We consider the new divisor 192 and the new remainder 104, and apply the division lemma to get
192 = 104 x 1 + 88
We consider the new divisor 104 and the new remainder 88,and apply the division lemma to get
104 = 88 x 1 + 16
We consider the new divisor 88 and the new remainder 16,and apply the division lemma to get
88 = 16 x 5 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 488 and 680 is 8
Notice that 8 = HCF(16,8) = HCF(88,16) = HCF(104,88) = HCF(192,104) = HCF(488,192) = HCF(680,488) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 974 > 8, we apply the division lemma to 974 and 8, to get
974 = 8 x 121 + 6
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 6 and 8, to get
8 = 6 x 1 + 2
Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 974 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(974,8) .
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Frequently Asked Questions on HCF of 488, 680, 974 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 488, 680, 974?
Answer: HCF of 488, 680, 974 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 488, 680, 974 using Euclid's Algorithm?
Answer: For arbitrary numbers 488, 680, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.