Highest Common Factor of 720, 152 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 720, 152 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 720, 152 is 8 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 720, 152 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 720, 152 is 8.
HCF(720, 152) = 8
HCF of 720, 152 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 720, 152 is 8.
Highest Common Factor of 720,152 is 8
Step 1: Since 720 > 152, we apply the division lemma to 720 and 152, to get
720 = 152 x 4 + 112
Step 2: Since the reminder 152 ≠ 0, we apply division lemma to 112 and 152, to get
152 = 112 x 1 + 40
Step 3: We consider the new divisor 112 and the new remainder 40, and apply the division lemma to get
112 = 40 x 2 + 32
We consider the new divisor 40 and the new remainder 32,and apply the division lemma to get
40 = 32 x 1 + 8
We consider the new divisor 32 and the new remainder 8,and apply the division lemma to get
32 = 8 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 720 and 152 is 8
Notice that 8 = HCF(32,8) = HCF(40,32) = HCF(112,40) = HCF(152,112) = HCF(720,152) .
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Frequently Asked Questions on HCF of 720, 152 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 720, 152?
Answer: HCF of 720, 152 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 720, 152 using Euclid's Algorithm?
Answer: For arbitrary numbers 720, 152 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
