Highest Common Factor of 9373, 1680, 40972 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 9373, 1680, 40972 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9373, 1680, 40972 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 9373, 1680, 40972 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 9373, 1680, 40972 is 1.
HCF(9373, 1680, 40972) = 1
HCF of 9373, 1680, 40972 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9373, 1680, 40972 is 1.
Highest Common Factor of 9373,1680,40972 is 1
Step 1: Since 9373 > 1680, we apply the division lemma to 9373 and 1680, to get
9373 = 1680 x 5 + 973
Step 2: Since the reminder 1680 ≠ 0, we apply division lemma to 973 and 1680, to get
1680 = 973 x 1 + 707
Step 3: We consider the new divisor 973 and the new remainder 707, and apply the division lemma to get
973 = 707 x 1 + 266
We consider the new divisor 707 and the new remainder 266,and apply the division lemma to get
707 = 266 x 2 + 175
We consider the new divisor 266 and the new remainder 175,and apply the division lemma to get
266 = 175 x 1 + 91
We consider the new divisor 175 and the new remainder 91,and apply the division lemma to get
175 = 91 x 1 + 84
We consider the new divisor 91 and the new remainder 84,and apply the division lemma to get
91 = 84 x 1 + 7
We consider the new divisor 84 and the new remainder 7,and apply the division lemma to get
84 = 7 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 9373 and 1680 is 7
Notice that 7 = HCF(84,7) = HCF(91,84) = HCF(175,91) = HCF(266,175) = HCF(707,266) = HCF(973,707) = HCF(1680,973) = HCF(9373,1680) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 40972 > 7, we apply the division lemma to 40972 and 7, to get
40972 = 7 x 5853 + 1
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 1 and 7, to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 40972 is 1
Notice that 1 = HCF(7,1) = HCF(40972,7) .
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Frequently Asked Questions on HCF of 9373, 1680, 40972 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 9373, 1680, 40972?
Answer: HCF of 9373, 1680, 40972 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9373, 1680, 40972 using Euclid's Algorithm?
Answer: For arbitrary numbers 9373, 1680, 40972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.