Highest Common Factor of 870, 232, 983 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 870, 232, 983 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 232, 983 is 1 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 870, 232, 983 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 870, 232, 983 is 1.
HCF(870, 232, 983) = 1
HCF of 870, 232, 983 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 870, 232, 983 is 1.
Highest Common Factor of 870,232,983 is 1
Step 1: Since 870 > 232, we apply the division lemma to 870 and 232, to get
870 = 232 x 3 + 174
Step 2: Since the reminder 232 ≠ 0, we apply division lemma to 174 and 232, to get
232 = 174 x 1 + 58
Step 3: We consider the new divisor 174 and the new remainder 58, and apply the division lemma to get
174 = 58 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 58, the HCF of 870 and 232 is 58
Notice that 58 = HCF(174,58) = HCF(232,174) = HCF(870,232) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 983 > 58, we apply the division lemma to 983 and 58, to get
983 = 58 x 16 + 55
Step 2: Since the reminder 58 ≠ 0, we apply division lemma to 55 and 58, to get
58 = 55 x 1 + 3
Step 3: We consider the new divisor 55 and the new remainder 3, and apply the division lemma to get
55 = 3 x 18 + 1
We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 58 and 983 is 1
Notice that 1 = HCF(3,1) = HCF(55,3) = HCF(58,55) = HCF(983,58) .
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Frequently Asked Questions on HCF of 870, 232, 983 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 870, 232, 983?
Answer: HCF of 870, 232, 983 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 232, 983 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 232, 983 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.