Highest Common Factor of 7152, 3370 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 7152, 3370 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7152, 3370 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 7152, 3370 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 7152, 3370 is 2.
HCF(7152, 3370) = 2
HCF of 7152, 3370 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7152, 3370 is 2.
Highest Common Factor of 7152,3370 is 2
Step 1: Since 7152 > 3370, we apply the division lemma to 7152 and 3370, to get
7152 = 3370 x 2 + 412
Step 2: Since the reminder 3370 ≠ 0, we apply division lemma to 412 and 3370, to get
3370 = 412 x 8 + 74
Step 3: We consider the new divisor 412 and the new remainder 74, and apply the division lemma to get
412 = 74 x 5 + 42
We consider the new divisor 74 and the new remainder 42,and apply the division lemma to get
74 = 42 x 1 + 32
We consider the new divisor 42 and the new remainder 32,and apply the division lemma to get
42 = 32 x 1 + 10
We consider the new divisor 32 and the new remainder 10,and apply the division lemma to get
32 = 10 x 3 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7152 and 3370 is 2
Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(42,32) = HCF(74,42) = HCF(412,74) = HCF(3370,412) = HCF(7152,3370) .
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Frequently Asked Questions on HCF of 7152, 3370 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 7152, 3370?
Answer: HCF of 7152, 3370 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7152, 3370 using Euclid's Algorithm?
Answer: For arbitrary numbers 7152, 3370 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.